In this paper,the estimation for a class of generalized varying coefficient models with error-prone covariates is considered.By combining basis function approximations with some auxiliary variables,an instrumental var...In this paper,the estimation for a class of generalized varying coefficient models with error-prone covariates is considered.By combining basis function approximations with some auxiliary variables,an instrumental variable type estimation procedure is proposed.The asymptotic results of the estimator,such as the consistency and the weak convergence rate,are obtained.The proposed procedure can attenuate the effect of measurement errors and have proved workable for finite samples.展开更多
In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose a...In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.展开更多
Very recently, Yu, Le and Zhou introduced the so called △B1^＊ and △B2^＊ conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the...Very recently, Yu, Le and Zhou introduced the so called △B1^＊ and △B2^＊ conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series. In fact, the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series, where coefficients may have different signs.展开更多
In this paper we study the asymptotic expansions of the solutions for a class of second order ordinary differential equations with slowly varying coefficients. The defect of the known works on these problems is noted,...In this paper we study the asymptotic expansions of the solutions for a class of second order ordinary differential equations with slowly varying coefficients. The defect of the known works on these problems is noted, and the results in [1 - 4] are improved and extended by means of the modified method of multiple scales.展开更多
In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero c...In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.展开更多
The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields,such as demography,epidemiology,regional economics,and psychology.With the deepening of...The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields,such as demography,epidemiology,regional economics,and psychology.With the deepening of research,some scholars find that there are some model specifications in spatial econometrics,such as spatial autoregressive(SAR)model and matrix exponential spatial specification(MESS),which cannot be nested within each other.Compared with the common SAR models,the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maximum likelihood estimation and Bayesian estimation.Meanwhile,MESS models have theoretical advantages.However,the theoretical research and application of MESS models have not been promoted vigorously.Therefore,the study of MESS model theory has practical significance.This paper studies the quasi maximum likelihood estimation for matrix exponential spatial specification(MESS)varying coefficient panel data models with fixed effects.It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymptotic normality to make a further supplement for the theoretical study of MESS model.展开更多
In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properti...In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.展开更多
Feature selection is a changing issue for varying coefficient models when the dimensionality of covariates is ultrahigh.The traditional technology of significantly reducing dimensionality is the marginal correlation s...Feature selection is a changing issue for varying coefficient models when the dimensionality of covariates is ultrahigh.The traditional technology of significantly reducing dimensionality is the marginal correlation screening method based on nonparametric smoothing.However,marginal correlation screening methods may be screen out variables that are jointly correlated to the response.To address this,we propose a novel screener with the name of group screening via nonparametric smoothing highdimensional ordinary least squares projection,referred to as“Group HOLP”and study its sure screening property.Based on this nice property,we introduce a refined feature selection procedure via employing the extended Bayesian information criteria(EBIC)to select the suitable submodels in varying coefficient models,which is coined as Group HOLP-EBIC method.Under some regularity conditions,we establish the strong consistency of feature selection for the proposed method.The performance of our method is evaluated by simulations and further illustrated by two real examples.展开更多
A one-step method is proposed to estimate the unknown functions in the varying coefficient models,in which the unknown functions admit different degrees of smoothness.In this method polynomials of different orders are...A one-step method is proposed to estimate the unknown functions in the varying coefficient models,in which the unknown functions admit different degrees of smoothness.In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness.As only one minimization operation is employed,the required computation burden is much less than that required by the existing two-step estimation method.It is shown that the one-step estimators also achieve the optimal convergence rate.Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method.More importantly,as only one minimization operation is employed,the full asymptotic properties,not only the asymptotic bias and variance,but also the asymptotic distributions of the estimators can be derived.The asymptotic distribution results will play a key role for making statistical inference.展开更多
We consider the problem of variable selection for the fixed effects varying coefficient models. A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions,...We consider the problem of variable selection for the fixed effects varying coefficient models. A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions, and the fixed effects are removed using the proper weight matrices. The proposed procedure simultaneously removes the fixed individual effects, selects the significant variables and estimates the nonzero coefficient functions. With appropriate selection of the tuning parameters, an asymptotic theory for the resulting estimates is established under suitable conditions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed for further illustration.展开更多
The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic ...The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.展开更多
Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es-timating the unknown functions ...Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es-timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time-dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.展开更多
This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Unde...This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.展开更多
In this letter, exact chirped multi-soliton solutions of the nonlinear Schrodinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, ...In this letter, exact chirped multi-soliton solutions of the nonlinear Schrodinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, an exponential distributed control system is considered, and some main features of solutions are shown. The results reveal that chirped soliton can all be nonlinearly compressed cleanly and efficiently in an optical fiber with no loss or gain, with the loss, or with the gain. Furthermore, under the same initial condition, compression of optical soliton in the optical fiber with the loss is the most dramatic. Also, under nonintegrable condition and finite initial perturbations, the evolution of chirped soliton has been demonstrated by simulating numerically.展开更多
In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated.An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are ...In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated.An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameters of interest. Finite sample performance of the proposed method is illustrated in a simulation study. The proposed methods are applied to an AIDS clinical trial dataset.展开更多
The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some sp...The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.展开更多
In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, d...In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.展开更多
Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and...Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.展开更多
In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least ...In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.展开更多
Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper ...Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data.The proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant coefficients.It is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient models.Under regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients.The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically normal.Finally,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis.The results show that the proposed method performs better than the existing competitor.展开更多
基金Supported by the National Natural Science Foundation of China(11101119)the Natural Science Foundation of Guangxi(2010GXNSFB013051)the Philosophy and Social Sciences Foundation of Guangxi(11FTJ002)
文摘In this paper,the estimation for a class of generalized varying coefficient models with error-prone covariates is considered.By combining basis function approximations with some auxiliary variables,an instrumental variable type estimation procedure is proposed.The asymptotic results of the estimator,such as the consistency and the weak convergence rate,are obtained.The proposed procedure can attenuate the effect of measurement errors and have proved workable for finite samples.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1110111911126332)+2 种基金the National Social Science Foundation of China(Grant No.11CTJ004)the Natural Science Foundation of Guangxi Province(Grant No.2010GXNSFB013051)the Philosophy and Social Sciences Foundation of Guangxi Province(Grant No.11FTJ002)
文摘In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.
基金Supported by National Natural Science Foundation of China (10901044)
文摘Very recently, Yu, Le and Zhou introduced the so called △B1^＊ and △B2^＊ conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series. In fact, the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series, where coefficients may have different signs.
基金The Project Supported by the National Natural Science Foundation of China
文摘In this paper we study the asymptotic expansions of the solutions for a class of second order ordinary differential equations with slowly varying coefficients. The defect of the known works on these problems is noted, and the results in [1 - 4] are improved and extended by means of the modified method of multiple scales.
文摘In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.
基金supported by the Innovation Project of Guangxi Graduate Education(YCSW2021073).
文摘The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields,such as demography,epidemiology,regional economics,and psychology.With the deepening of research,some scholars find that there are some model specifications in spatial econometrics,such as spatial autoregressive(SAR)model and matrix exponential spatial specification(MESS),which cannot be nested within each other.Compared with the common SAR models,the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maximum likelihood estimation and Bayesian estimation.Meanwhile,MESS models have theoretical advantages.However,the theoretical research and application of MESS models have not been promoted vigorously.Therefore,the study of MESS model theory has practical significance.This paper studies the quasi maximum likelihood estimation for matrix exponential spatial specification(MESS)varying coefficient panel data models with fixed effects.It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymptotic normality to make a further supplement for the theoretical study of MESS model.
基金supported by the National Natural Science Foundation of China(No.12571284,No.12171203)supported by the National Natural Science Foundation of China(No.12561051)+3 种基金the Fundamental Research Funds for the Central Universities(No.23JNQMX21)supported by the University-level scientific research project of Guangdong University of Foreign Studies(NO.299-GK25G301/25TS10)supported by a grant from National Natural Foundation of China(No.12171225)Yunnan Province Xing Dian Talent Support Program(YNWR-YLXZ-2018-020)。
文摘In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.
文摘Feature selection is a changing issue for varying coefficient models when the dimensionality of covariates is ultrahigh.The traditional technology of significantly reducing dimensionality is the marginal correlation screening method based on nonparametric smoothing.However,marginal correlation screening methods may be screen out variables that are jointly correlated to the response.To address this,we propose a novel screener with the name of group screening via nonparametric smoothing highdimensional ordinary least squares projection,referred to as“Group HOLP”and study its sure screening property.Based on this nice property,we introduce a refined feature selection procedure via employing the extended Bayesian information criteria(EBIC)to select the suitable submodels in varying coefficient models,which is coined as Group HOLP-EBIC method.Under some regularity conditions,we establish the strong consistency of feature selection for the proposed method.The performance of our method is evaluated by simulations and further illustrated by two real examples.
文摘A one-step method is proposed to estimate the unknown functions in the varying coefficient models,in which the unknown functions admit different degrees of smoothness.In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness.As only one minimization operation is employed,the required computation burden is much less than that required by the existing two-step estimation method.It is shown that the one-step estimators also achieve the optimal convergence rate.Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method.More importantly,as only one minimization operation is employed,the full asymptotic properties,not only the asymptotic bias and variance,but also the asymptotic distributions of the estimators can be derived.The asymptotic distribution results will play a key role for making statistical inference.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471029,11101014 and 11301279)the Beijing Natural Science Foundation(Grant No.1142002+3 种基金the Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.12KJB110016)CERG Grant from the Hong Kong Research Grants Council(Grant No.HKBU 202012)FRG Grant from Hong Kong Baptist University(Grant No.FRG2/12-13/077)
文摘We consider the problem of variable selection for the fixed effects varying coefficient models. A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions, and the fixed effects are removed using the proper weight matrices. The proposed procedure simultaneously removes the fixed individual effects, selects the significant variables and estimates the nonzero coefficient functions. With appropriate selection of the tuning parameters, an asymptotic theory for the resulting estimates is established under suitable conditions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed for further illustration.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609+1 种基金the Doctor's Start-up Research Fund under Grant No. 08-52204the Youth Science Research Fund of Chongging Technology and Business University under Grant No. 0852008
文摘The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.
基金Research Foundation for Doctor Programme(Grant No.20060254006)the National Natural Science Foundation of China(Grant No.10671089)
文摘Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es-timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time-dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.
基金supported by National Natural Science Foundation of China (Grant No. 10671089)China Postdoctoral Science Foundation and Jiangsu Planned Projects for Postdoctoral Research Funds
文摘This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.
基金This work was supported by the National Natural Science Foundation of China (No. 60477026), the Provincial Youth Science Foundation of Shanxi (No. 20011015).
文摘In this letter, exact chirped multi-soliton solutions of the nonlinear Schrodinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, an exponential distributed control system is considered, and some main features of solutions are shown. The results reveal that chirped soliton can all be nonlinearly compressed cleanly and efficiently in an optical fiber with no loss or gain, with the loss, or with the gain. Furthermore, under the same initial condition, compression of optical soliton in the optical fiber with the loss is the most dramatic. Also, under nonintegrable condition and finite initial perturbations, the evolution of chirped soliton has been demonstrated by simulating numerically.
基金Supported by National Social Science Foundation of China(16BTJ015)
文摘In this paper, a varying coefficient errors-in-variables model under longitudinal data is investigated.An empirical likelihood based bias-correction approach is proposed. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameters of interest. Finite sample performance of the proposed method is illustrated in a simulation study. The proposed methods are applied to an AIDS clinical trial dataset.
基金supported by National Natural Science Foundation of China (Grant Nos. 11401006, 11671299 and 11671042)a grant from the University Grants Council of Hong Kong+1 种基金the China Postdoctoral Science Foundation (Grant No. 2017M611083)the National Statistical Science Research Program of China (Grant No. 2015LY55)
文摘The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.
基金Supported by National Natural Science Foundation of China(Grant Nos.11501522,11101014,11001118 and11171012)National Statistical Research Projects(Grant No.2014LZ45)+2 种基金the Doctoral Fund of Innovation of Beijing University of Technologythe Science and Technology Project of the Faculty Adviser of Excellent PhD Degree Thesis of Beijing(Grant No.20111000503)the Beijing Municipal Education Commission Foundation(Grant No.KM201110005029)
文摘In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.
基金Supported by the National Natural Science Foundation of China (No. 10871177)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20090101110020)
文摘Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.
基金Supported by the Educational Commission of Hubei Province of China(Grant No.D20112503)National Natural Science Foundation of China(Grant Nos.11071022,11231010 and 11028103)the foundation of Beijing Center of Mathematics and Information Sciences
文摘In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.
基金supported in part by the National Science Foundation of China under Grant Nos.12071305and 71803001in part by the national social science foundation of China under Grant No.19BTJ014+1 种基金in part by the University Social Science Research Project of Anhui Province under Grant No.SK2020A0051in part by the Social Science Foundation of the Ministry of Education of China under Grant Nos.19YJCZH250 and 21YJAZH081。
文摘Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data.The proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant coefficients.It is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient models.Under regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients.The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically normal.Finally,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis.The results show that the proposed method performs better than the existing competitor.
