The Annals of Statistics

Efficient estimation of a semiparametric partially linear varying coefficient model

Ibrahim Ahmad, Sittisak Leelahanon, and Qi Li

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Abstract

In this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model. We establish the consistency and $\sqrt{n}$-normality property of the estimator of the finite-dimensional parameters of the model. We further show that, when the error is conditionally homoskedastic, this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite-dimensional parameter reaches the semiparametric efficiency bound of this model. A small-scale simulation is reported to examine the finite sample performance of the proposed estimator, and an empirical application is presented to illustrate the usefulness of the proposed method in practice. We also discuss how to obtain an efficient estimation result when the error is conditional heteroskedastic.

Article information

Source
Ann. Statist., Volume 33, Number 1 (2005), 258-283.

Dates
First available in Project Euclid: 8 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1112967706

Digital Object Identifier
doi:10.1214/009053604000000931

Mathematical Reviews number (MathSciNet)
MR2157803

Zentralblatt MATH identifier
1064.62043

Subjects
Primary: 62G08: Nonparametric regression

Keywords
Series estimation method partially linear varying coefficient asymptotic normality semiparametric efficiency

Citation

Ahmad, Ibrahim; Leelahanon, Sittisak; Li, Qi. Efficient estimation of a semiparametric partially linear varying coefficient model. Ann. Statist. 33 (2005), no. 1, 258--283. doi:10.1214/009053604000000931. https://projecteuclid.org/euclid.aos/1112967706


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