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February 2020 Two-step semiparametric empirical likelihood inference
Francesco Bravo, Juan Carlos Escanciano, Ingrid Van Keilegom
Ann. Statist. 48(1): 1-26 (February 2020). DOI: 10.1214/18-AOS1788

Abstract

In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods.

Citation

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Francesco Bravo. Juan Carlos Escanciano. Ingrid Van Keilegom. "Two-step semiparametric empirical likelihood inference." Ann. Statist. 48 (1) 1 - 26, February 2020. https://doi.org/10.1214/18-AOS1788

Information

Received: 1 January 2018; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196527
MathSciNet: MR4065150
Digital Object Identifier: 10.1214/18-AOS1788

Subjects:
Primary: 62M10
Secondary: 62G10

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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