In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; ...In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.展开更多
This paper studies evolutionary mechanism of parameter selection in the construction of weight function for Nearest Neighbour Estimate in nonparametric regression. Construct an algorithm which adaptively evolves fine ...This paper studies evolutionary mechanism of parameter selection in the construction of weight function for Nearest Neighbour Estimate in nonparametric regression. Construct an algorithm which adaptively evolves fine weight and makes good prediction about unknown points. The numerical experiments indicate that this method is effective. It is a meaningful discussion about practicability of nonparametric regression and methodology of adaptive model-building.展开更多
A K-nearest neighbor （K-NN） based nonparametric regression model was proposed to predict travel speed for Beijing expressway. By using the historical traffic data collected from the detectors in Beijing expressways,...A K-nearest neighbor （K-NN） based nonparametric regression model was proposed to predict travel speed for Beijing expressway. By using the historical traffic data collected from the detectors in Beijing expressways, a specically designed database was developed via the processes including data filtering, wavelet analysis and clustering. The relativity based weighted Euclidean distance was used as the distance metric to identify the K groups of nearest data series. Then, a K-NN nonparametric regression model was built to predict the average travel speeds up to 6 min into the future. Several randomly selected travel speed data series, collected from the floating car data （FCD） system, were used to validate the model. The results indicate that using the FCD, the model can predict average travel speeds with an accuracy of above 90%, and hence is feasible and effective.展开更多
This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of...This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.展开更多
The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this...The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this paper, a simple test for heteroscedasticity is proposed in nonparametric regression based on residual analysis. Furthermore, some simulations with a comparison with Dette and Munk＇s method are conducted to evaluate the performance of the proposed test. The results demonstrate that the method in this paper performs quite satisfactorily and is much more powerful than Dette and Munk＇s method in some cases.展开更多
In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete co...In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.展开更多
We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warp...We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.展开更多
For the nonparametric regression model Y-ni = g(x(ni)) + epsilon(ni)i = 1, ..., n, with regularly spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold ...For the nonparametric regression model Y-ni = g(x(ni)) + epsilon(ni)i = 1, ..., n, with regularly spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold and truncation parameters are chosen by cross-validation on the everage squared error, strong consistency for the case of dyadic sample size and moment consistency for arbitrary sample size are established under some regular conditions.展开更多
Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densi...Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion.展开更多
This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying...This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.展开更多
In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-depend...The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.展开更多
In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by ...In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.展开更多
This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their res...This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their respective marginal regression functions (RV-SIS). We show that, under some mild technical conditions, the RV-SIS possesses a sure screening property, which is defined by Fan and Lv (2008). Numerical comparisons suggest that RV-SIS has competitive performance compared to other screening procedures, and outperforms them in many different model settings.展开更多
In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some gen...In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.展开更多
This paper introduces several alternative statistical approaches to modeling and prediction of electric energy generated by photovoltaic farms. The statistical models use outputs of a numerical weather prediction mode...This paper introduces several alternative statistical approaches to modeling and prediction of electric energy generated by photovoltaic farms. The statistical models use outputs of a numerical weather prediction model as their inputs. Presented statistical models allow for easy-to-compute predictions, both in temporal sense and for out-of-sample individual farms. Model performance is illustrated on a sample of real photovoltaic farms located in the Czech Republic.展开更多
The objective of this study is to examine the use of the conditional probability function(CPF) and nonparametric regression(NPR) to identify the relationship between wind direction and concentration of PM2.5(particula...The objective of this study is to examine the use of the conditional probability function(CPF) and nonparametric regression(NPR) to identify the relationship between wind direction and concentration of PM2.5(particulate matter with aerodynamic diameter less than or equal to 2.5 μm). Twenty four-hour integrated PM2.5 mass and species concentrations were measured at the St. Louis-Midwest Supersite in East St. Louis,Illinois,USA in the periods of 22-28 June 2001,7-13 November 2001,and 19-25 March 2002. Wind directions were measured on site. The concentrations of 15 elements and ions,i.e. Al,As,Cd,Cr,Cu,Fe,Mn,Ni,Pb,Se,Zn,OC,EC,SO4,and NO3 were calculated using the CPF and NPR. The comparison between the results obtained from the CPF and NPR demonstrated that they both agreed well with the locations of the known local point sources. The CPF was simpler and easier to calculate than NPR. In contrast,NPR provided PM2.5 concentrations but with some uncertainties. This study indicates that both methods can be utilized to promote the source apportionment study of ambient PM2.5.展开更多
This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong...This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.展开更多
Consider the nonparametric median regression model Y-ni = g(x(ni)) + epsilon(ni), 1 less than or equal to i less than or equal to n, where Y-ni's are the observations at the fixed design points x(ni) is an element...Consider the nonparametric median regression model Y-ni = g(x(ni)) + epsilon(ni), 1 less than or equal to i less than or equal to n, where Y-ni's are the observations at the fixed design points x(ni) is an element of [0, 1], is an element of(ni)'s are independent identically distributed random variables with median zero, g(x) is the smooth function of interest, Suppose the local median estimate (g) over tilde(n, h)(x) of g(x) admits the Bahadur's representation. Under some regular conditions, the relative stability of the local median estimate is established in the L-2 sense.展开更多
In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data.Based on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we const...In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data.Based on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we construct the NW and LL estimators of the conditional quantile.Under strong mixing assumptions,we establish asymptotic representation and asymptotic normality of the estimators.Finite sample behavior of the estimators is investigated via simulation,and a real data example is used to illustrate the application of the proposed methods.展开更多
基金Supported by the Science Development Foundation of HFUT(041002F)
文摘In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.
文摘This paper studies evolutionary mechanism of parameter selection in the construction of weight function for Nearest Neighbour Estimate in nonparametric regression. Construct an algorithm which adaptively evolves fine weight and makes good prediction about unknown points. The numerical experiments indicate that this method is effective. It is a meaningful discussion about practicability of nonparametric regression and methodology of adaptive model-building.
基金The Project of Research on Technologyand Devices for Traffic Guidance (Vehicle Navigation)System of Beijing Municipal Commission of Science and Technology(No H030630340320)the Project of Research on theIntelligence Traffic Information Platform of Beijing Education Committee
文摘A K-nearest neighbor （K-NN） based nonparametric regression model was proposed to predict travel speed for Beijing expressway. By using the historical traffic data collected from the detectors in Beijing expressways, a specically designed database was developed via the processes including data filtering, wavelet analysis and clustering. The relativity based weighted Euclidean distance was used as the distance metric to identify the K groups of nearest data series. Then, a K-NN nonparametric regression model was built to predict the average travel speeds up to 6 min into the future. Several randomly selected travel speed data series, collected from the floating car data （FCD） system, were used to validate the model. The results indicate that using the FCD, the model can predict average travel speeds with an accuracy of above 90%, and hence is feasible and effective.
基金This paper is supported by NNSF project(10371059)China and Youth Teacher Foundation of Nankai University
文摘This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.
基金the National Natural Science Foundation of China (10531030)
文摘The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this paper, a simple test for heteroscedasticity is proposed in nonparametric regression based on residual analysis. Furthermore, some simulations with a comparison with Dette and Munk＇s method are conducted to evaluate the performance of the proposed test. The results demonstrate that the method in this paper performs quite satisfactorily and is much more powerful than Dette and Munk＇s method in some cases.
基金Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201310357004,201410357117,201410357249)Supported by the Quality Improvement Projects for Undergraduate Education of Anhui University(ZLTS2015035)
文摘In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.
文摘We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.
文摘For the nonparametric regression model Y-ni = g(x(ni)) + epsilon(ni)i = 1, ..., n, with regularly spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold and truncation parameters are chosen by cross-validation on the everage squared error, strong consistency for the case of dyadic sample size and moment consistency for arbitrary sample size are established under some regular conditions.
基金Project Supported by National Natural Science Foundation of China.
文摘Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion.
文摘This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.
文摘In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
文摘The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.
文摘In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.
文摘This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their respective marginal regression functions (RV-SIS). We show that, under some mild technical conditions, the RV-SIS possesses a sure screening property, which is defined by Fan and Lv (2008). Numerical comparisons suggest that RV-SIS has competitive performance compared to other screening procedures, and outperforms them in many different model settings.
基金Supported by the National Natural Science Foundation of China(11501004,11501005,11526033,11671012)the Natural Science Foundation of Anhui Province(1508085J06,1608085QA02)+1 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)
文摘In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.
文摘This paper introduces several alternative statistical approaches to modeling and prediction of electric energy generated by photovoltaic farms. The statistical models use outputs of a numerical weather prediction model as their inputs. Presented statistical models allow for easy-to-compute predictions, both in temporal sense and for out-of-sample individual farms. Model performance is illustrated on a sample of real photovoltaic farms located in the Czech Republic.
基金supported by the National Natural Science Foundation of China under the grant number 40675060, 2006AA09Z151 program of the Ministry of Science and Technology of the People’s Republic of China, and GYHY200706031 program of China Meteorological Administration.
文摘The objective of this study is to examine the use of the conditional probability function(CPF) and nonparametric regression(NPR) to identify the relationship between wind direction and concentration of PM2.5(particulate matter with aerodynamic diameter less than or equal to 2.5 μm). Twenty four-hour integrated PM2.5 mass and species concentrations were measured at the St. Louis-Midwest Supersite in East St. Louis,Illinois,USA in the periods of 22-28 June 2001,7-13 November 2001,and 19-25 March 2002. Wind directions were measured on site. The concentrations of 15 elements and ions,i.e. Al,As,Cd,Cr,Cu,Fe,Mn,Ni,Pb,Se,Zn,OC,EC,SO4,and NO3 were calculated using the CPF and NPR. The comparison between the results obtained from the CPF and NPR demonstrated that they both agreed well with the locations of the known local point sources. The CPF was simpler and easier to calculate than NPR. In contrast,NPR provided PM2.5 concentrations but with some uncertainties. This study indicates that both methods can be utilized to promote the source apportionment study of ambient PM2.5.
基金The first author’s research was supported by the National Natural Science Foundation of China(Grant No.198310110 and Grant No.19871003)the partly support of the Doctoral Foundation of China and the last three authors’research was supported by a gra
文摘This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.
文摘Consider the nonparametric median regression model Y-ni = g(x(ni)) + epsilon(ni), 1 less than or equal to i less than or equal to n, where Y-ni's are the observations at the fixed design points x(ni) is an element of [0, 1], is an element of(ni)'s are independent identically distributed random variables with median zero, g(x) is the smooth function of interest, Suppose the local median estimate (g) over tilde(n, h)(x) of g(x) admits the Bahadur's representation. Under some regular conditions, the relative stability of the local median estimate is established in the L-2 sense.
基金supported by the National Natural Science Foundation of China(12071348)the Key Scientific Research Foundation of Henan Educational Committee(24A110001)Key Laboratory of Intelligent Computing and Applications(Ministry of Education),Tongji University,China.
文摘In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data.Based on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we construct the NW and LL estimators of the conditional quantile.Under strong mixing assumptions,we establish asymptotic representation and asymptotic normality of the estimators.Finite sample behavior of the estimators is investigated via simulation,and a real data example is used to illustrate the application of the proposed methods.
