Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model an...Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.展开更多
As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correla...As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.展开更多
To improve the prediction accuracy of semiparametric additive partial linear models(APLM) and the coverage probability of confidence intervals of the parameters of interest,we explore a focused information criterion f...To improve the prediction accuracy of semiparametric additive partial linear models(APLM) and the coverage probability of confidence intervals of the parameters of interest,we explore a focused information criterion for model selection among ALPM after we estimate the nonparametric functions by the polynomial spline smoothing,and introduce a general model average estimator.The major advantage of the proposed procedures is that iterative backfitting implementation is avoided,which thus results in gains in computational simplicity.The resulting estimators are shown to be asymptotically normal.A simulation study and a real data analysis are presented for illustrations.展开更多
This paper proposed a general framework based on semiparametric additive mixed effects model to identify subgroups on each covariate and estimate the corresponding regression functions simultaneously for longitudinal ...This paper proposed a general framework based on semiparametric additive mixed effects model to identify subgroups on each covariate and estimate the corresponding regression functions simultaneously for longitudinal data,thus it could reveal which covariate contributes to the existence of subgroups among population.A backfitting combined with k-means algorithm was developed to detect subgroup structure on each covariate and estimate each semiparametric additive component across subgroups.A Bayesian information criterion is employed to estimate the actual number of groups.The efficacy and accuracy of the proposed procedure in identifying the subgroups and estimating the regression functions are illustrated through numerical studies.In addition,the authors demonstrate the usefulness of the proposed method with applications to PBC data and Industrial Portfolio's Return data and provide meaningful partitions of the populations.展开更多
The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear sche...The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10561008, 10761011)Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. Y200805073)+1 种基金PhD Special Scientific Research Foundation of Chinese University (Grant No. 20060673002)Program for New Century Excellent Talents in University (Grant No. NCET-07-0737)
文摘Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
基金Chuanhua Wei’s research was supported by the National Natural Science Foundation of China(11301565)Jin Yang’s research was supported by the Post-doctoral Fellowship of Nankai University
文摘As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.
基金supported by US National Science Foundation (Grant No.DMS-0806097)
文摘To improve the prediction accuracy of semiparametric additive partial linear models(APLM) and the coverage probability of confidence intervals of the parameters of interest,we explore a focused information criterion for model selection among ALPM after we estimate the nonparametric functions by the polynomial spline smoothing,and introduce a general model average estimator.The major advantage of the proposed procedures is that iterative backfitting implementation is avoided,which thus results in gains in computational simplicity.The resulting estimators are shown to be asymptotically normal.A simulation study and a real data analysis are presented for illustrations.
基金supported in part by the National Natural Science Foundation of China under Grant No.12171450。
文摘This paper proposed a general framework based on semiparametric additive mixed effects model to identify subgroups on each covariate and estimate the corresponding regression functions simultaneously for longitudinal data,thus it could reveal which covariate contributes to the existence of subgroups among population.A backfitting combined with k-means algorithm was developed to detect subgroup structure on each covariate and estimate each semiparametric additive component across subgroups.A Bayesian information criterion is employed to estimate the actual number of groups.The efficacy and accuracy of the proposed procedure in identifying the subgroups and estimating the regression functions are illustrated through numerical studies.In addition,the authors demonstrate the usefulness of the proposed method with applications to PBC data and Industrial Portfolio's Return data and provide meaningful partitions of the populations.
基金supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y6110662)
文摘The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.
