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Confidence Intervals of Variance Functions in Generalized Linear Model

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Abstract

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 nonparametric autoregressive times series model with heteroscedastic conditional variance.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Yong Zhou & Dao-ji Li

Authors
  1. Yong Zhou
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  2. Dao-ji Li
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Correspondence to Yong Zhou.

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

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Zhou, Y., Li, Dj. Confidence Intervals of Variance Functions in Generalized Linear Model. Acta Math. Appl. Sin, Engl. Ser. 22, 353–368 (2006). https://doi.org/10.1007/s10255-006-0311-x

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  • DOI: https://doi.org/10.1007/s10255-006-0311-x

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