Sieve empirical likelihood and extensions of the generalized least squares

Zhang, J. and Gijbels, I. (2003) Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics, 30 (1). pp. 1-24. ISSN 0303-6898. (The full text of this publication is not available from this repository)

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Abstract

The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for estimation of constrained parametric or non-parametric regression models with unspecified error distributions. It shows some interesting connections with certain extensions of the generalized least squares approach. A general asymptotic theory is provided. In the parametric regression setting it is shown that under certain regularity conditions the proposed estimators are asymptotically efficient even if the restriction functions are discontinuous. In the non-parametric regression setting the convergence rate of the maximum estimator based on the sieve empirical likelihood is given. In both settings, it is shown that the estimator is adaptive for the inhomogeneity of conditional error distributions with respect to predictor, especially for heteroscedasticity.

Item Type: Article
Uncontrolled keywords: asymptotic efficiency; conditional equations; generalized least squares; generalized method of moments; semiparametric and non-parametric regressions; sieve empirical likelihood
Subjects: H Social Sciences > HA Statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:22
Last Modified: 15 Oct 2012 12:42
Resource URI: http://kar.kent.ac.uk/id/eprint/595 (The current URI for this page, for reference purposes)
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