Confidence Intervals of Variance Functions in Generalized Linear Model  

作　　者：Yong Zhou Dao-ji Li 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Acta Mathematicae Applicatae Sinica》2006年第3期353-368,共16页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China （No.10471140）.

摘　　要：In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.

关 键 词：Nonlinear time series model variance function conditional heteroscedastie variance generalized linear model local polynomial fitting Α-MIXING 

分 类 号：O17[理学—数学]