Bernoulli

  • Bernoulli
  • Volume 18, Number 3 (2012), 836-856.

Empirical likelihood for single-index varying-coefficient models

Liugen Xue and Qihua Wang

Full-text: Open access

Abstract

In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear fitting, then construct an estimated empirical likelihood ratio function and hence obtain a maximum empirical likelihood estimator for the parametric component. Our estimator for parametric component is asymptotically efficient, and the estimator of nonparametric component has an optimal convergence rate. Our results provide ways to construct the confidence region for the involved unknown parameter. We also develop an adjusted empirical likelihood ratio for constructing the confidence regions of parameters of interest. A simulation study is conducted to evaluate the finite sample behaviors of the proposed methods.

Article information

Source
Bernoulli, Volume 18, Number 3 (2012), 836-856.

Dates
First available in Project Euclid: 28 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1340887005

Digital Object Identifier
doi:10.3150/11-BEJ365

Mathematical Reviews number (MathSciNet)
MR2948904

Zentralblatt MATH identifier
1208.62062

Keywords
confidence region empirical likelihood nonparametric component parametric component single-index varying-coefficient model

Citation

Xue, Liugen; Wang, Qihua. Empirical likelihood for single-index varying-coefficient models. Bernoulli 18 (2012), no. 3, 836--856. doi:10.3150/11-BEJ365. https://projecteuclid.org/euclid.bj/1340887005


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