Efficient semiparametric estimator for heteroscedastic partially linear models

Yanyuan Ma, Jeng Min Chiou, Naisyin Wang

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

We study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function. An interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated. To avoid this, we propose a family of consistent estimators and investigate their asymptotic properties. We show that the optimal semiparametric efficiency bound can be reached by a semiparametric kernel estimator in this family. Building upon our theoretical findings and heuristic arguments about the equivalence between kernel and spline smoothing, we conjecture that a weighted partial-spline estimator could also be semiparametric efficient. Properties of the proposed estimators are presented through theoretical illustration and numerical simulations.

Original languageEnglish (US)
Pages (from-to)75-84
Number of pages10
JournalBiometrika
Volume93
Issue number1
DOIs
StatePublished - Mar 1 2006

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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