Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） ...Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.展开更多
In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonp...In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.展开更多
The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower...The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.展开更多
In the present paper as estimation of an unknown probability density of the spline-estimation is constructed, necessity and sufficiency conditions of strong consistency of the spline-estimation are given.
Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-li...Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.展开更多
This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG （2002） t...This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG （2002） to the NA errors without necessarily imposing any extra condition.展开更多
The strong consistency of M estimators of the regression parameters in linear models for ρ-mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results i...The strong consistency of M estimators of the regression parameters in linear models for ρ-mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu （2005） is improved essentially on the moment conditions.展开更多
This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models ...This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].展开更多
In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distributio...In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distribution. rate of modified （（Xi,Yi）,i 〉 1} .展开更多
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be est...In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.展开更多
Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing d...Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.展开更多
The parameter estimation and the coefficient of contamination for the regression models with repeated measures are studied when its response variables are contaminated by another random variable sequence.Under the sui...The parameter estimation and the coefficient of contamination for the regression models with repeated measures are studied when its response variables are contaminated by another random variable sequence.Under the suitable conditions it is proved that the estimators which are established in the paper are strongly consistent estimators.展开更多
In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the fin...In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the finite moment of order 2 only. The non parametric estimation of contaminated coefficient ε and regression parameter β are established, and the strong consistency and convergence rate almost surely of the estimators are obtained. A simulated example is also given to show the visual performance of the estimations.展开更多
In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function ...In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.展开更多
We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (...We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.展开更多
In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptot...In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.展开更多
This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second...This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second,we construct maximum likelihood estimators of these parameters and then discuss their strong consistency.Third,a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered.Finally,we estimate the errors between solutions of these equations and that of their numerical equations.展开更多
This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean cons...This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean consistency are obtained under a locally generallied Gaussinan error's structure. Finally, the author showes that the usual weight functions based on nearest neighbor method satisfy the deigned assumptions imposed.展开更多
Consider the partly linear model Y = xβ ＋ g（t） ＋ e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is a martingale difference sequence. Let ...Consider the partly linear model Y = xβ ＋ g（t） ＋ e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is a martingale difference sequence. Let ~ be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of {（Yj, xj, tj）n＋N j=n＋1 }, the independent validation data containing n observations of {（xj, x j, tj）n j=1 } is available. In this paper, a semiparametric method with the primary data is employed to obtain the estimator ofβ and g（-） based on the least squares criterion with the help of validation data. The proposed estimators are proved to be strongly consistent. Finite sample behavior of the estimators is investigated via simulations too.展开更多
基金Supported by the National Natural Sciences Foundation of China (10761011)Mathematical Tianyuan Fund of National Natural Science Fundation of China(10626048)
文摘Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.
基金Supported by the National Natural Science Foundation of China(10571008)Supported by the Natural Science Foundation of Henan(0511013300)Supported by the National Science Foundation of Henan Education Department(2006110012)
文摘In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.
基金The NSF (11201001,11171001,11126176) of Chinathe NSF (1208085QA03) of Anhui Province+2 种基金Provincial Natural Science Research Project (KJ2010A005) of Anhui CollegesDoctoral Research Start-up Funds Projects of Anhui Universitythe Students’ Innovative Training Project (2012003) of Anhui University
文摘The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.
文摘In the present paper as estimation of an unknown probability density of the spline-estimation is constructed, necessity and sufficiency conditions of strong consistency of the spline-estimation are given.
基金This work was supported by the National Natural Science Foundation of China.
文摘Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.
基金The research is supported by National Natural Science Foundation of China(No.10661006)the Support Program for 100 Young and Middle-aged Disciplinary Leaders in Guangxi Higher Education Institutions([2005]64),and Guangxi Science Foundation(0447096)
文摘This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG （2002） to the NA errors without necessarily imposing any extra condition.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 11061012, the Support Program of the New Century Guangxi China Ten-hundred-thousand Talents Project under Grant No. 2005214, and the Guangxi, China Science Foundation under Grant No. 0991081.
文摘The strong consistency of M estimators of the regression parameters in linear models for ρ-mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu （2005） is improved essentially on the moment conditions.
基金the Natural Science Foundation of Yunnan University （No. 2005Z007C） the Scientific Research Fund of Yunnan Provincial Education Department （No. 5Y0062A）+1 种基金 Mathematical Tianyuan Fund of National Natural Science Foundation of China （No. 10626048） Special Foundation for Middle and Young Excellent Teachers of Yunnan University.
文摘This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].
文摘In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distribution. rate of modified （（Xi,Yi）,i 〉 1} .
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
基金Supported by the National Natural Science Foundation of China (10571008)the Natural Science Foundation of Henan (092300410149)the Core Teacher Foundationof Henan (2006141)
文摘In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.
文摘Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.
文摘The parameter estimation and the coefficient of contamination for the regression models with repeated measures are studied when its response variables are contaminated by another random variable sequence.Under the suitable conditions it is proved that the estimators which are established in the paper are strongly consistent estimators.
文摘In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the finite moment of order 2 only. The non parametric estimation of contaminated coefficient ε and regression parameter β are established, and the strong consistency and convergence rate almost surely of the estimators are obtained. A simulated example is also given to show the visual performance of the estimations.
文摘In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.
文摘We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.
文摘In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.
基金supported by NSF of China(11001051,11371352,12071071)China Scholarship Council(201906095034).
文摘This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second,we construct maximum likelihood estimators of these parameters and then discuss their strong consistency.Third,a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered.Finally,we estimate the errors between solutions of these equations and that of their numerical equations.
文摘This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean consistency are obtained under a locally generallied Gaussinan error's structure. Finally, the author showes that the usual weight functions based on nearest neighbor method satisfy the deigned assumptions imposed.
基金Supported by National Natural Science Foundation of China(Grant Nos.1127115511371168+7 种基金110011051107112611071269)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20110061110003)the Natural Science Foundation of Jilin Province(Grant Nos.20130101066JC20130522102JH20101596)"Twelfth Five-Year Plan"Science and Technology Research Project of the Education Department of Jilin Province(Grant No.2012186)
文摘Consider the partly linear model Y = xβ ＋ g（t） ＋ e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is a martingale difference sequence. Let ~ be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of {（Yj, xj, tj）n＋N j=n＋1 }, the independent validation data containing n observations of {（xj, x j, tj）n j=1 } is available. In this paper, a semiparametric method with the primary data is employed to obtain the estimator ofβ and g（-） based on the least squares criterion with the help of validation data. The proposed estimators are proved to be strongly consistent. Finite sample behavior of the estimators is investigated via simulations too.
