Two-Step Semiparametric Empirical Likelihood Inference

Francesco Bravo, Juan Carlos Escanciano and Ingrid Ingrid Van Keilegom ()
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Ingrid Ingrid Van Keilegom: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2020046, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: Empirical likelihood; Semiparametric inference; Highdimensional parameters; Wilks’ phenomenon (search for similar items in EconPapers)
Date: 2020-01-01
Note: In: Annals of Statistics, Vol. 48, no. 1, p. 1-26 (2020)
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020046

DOI: 10.1214/18-AOS1788

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