Local quasi-likelihood estimation with data missing at random

Jianwei Chen, Jianqing Fan, Kim Hung Li, Haibo Zhou

Research output: Contribution to journalReview article

19 Scopus citations

Abstract

Local quasi-likelihood estimation is useful for nonparametric modeling in a widely-used exponential family of distributions, called generalized linear models. Yet, the technique cannot be directly applied to situations where a response variable is missing at random. Three local quasi-likelihood estimation techniques are introduced: the local quasi-likelihood estimator using only complete-data; the locally weighted quasi-likelihood method; the local quasi-likelihood estimator with imputed values. These estimators share basically the same first order asymptotic biases and variances. Our simulation results show that substantial efficiency gains can be obtained by using the local quasi-likelihood estimator with imputed values. We develop the local quasi-likelihood imputation methods for estimating the mean functional of the response variable. It is shown that the proposed mean imputation estimators are asymptotically normal with asymptotic variance that can be easily estimated. Data from an ongoing environmental epidemiologic study is used to illustrate the proposed methods.

Original languageEnglish (US)
Pages (from-to)1071-1100
Number of pages30
JournalStatistica Sinica
Volume16
Issue number4
StatePublished - Oct 1 2006

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Bandwidth selection
  • Generalized linear models
  • Local imputation method
  • Nonparametric regression
  • Quasi-likelihood
  • The mean functional

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