Efficient semiparametric estimator for heteroscedastic partially linear models

Yanyuan Ma, Jeng Min Chiou, Naisyin Wang

Research output: Contribution to journalArticle

42 Citations (Scopus)

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

Fingerprint

Partially Linear Model
Splines
Linear Models
linear models
Efficiency
Estimator
Baseline
seeds
Semiparametric Efficiency
Spline Smoothing
Partial
Kernel Smoothing
Variance Function
Kernel Estimator
Consistent Estimator
Asymptotic Properties
Spline
Computer simulation
Equivalence
Heuristics

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

Cite this

Ma, Yanyuan ; Chiou, Jeng Min ; Wang, Naisyin. / Efficient semiparametric estimator for heteroscedastic partially linear models. In: Biometrika. 2006 ; Vol. 93, No. 1. pp. 75-84.
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Efficient semiparametric estimator for heteroscedastic partially linear models. / Ma, Yanyuan; Chiou, Jeng Min; Wang, Naisyin.

In: Biometrika, Vol. 93, No. 1, 01.03.2006, p. 75-84.

Research output: Contribution to journalArticle

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