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Two-step semiparametric empirical likelihood inference

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2020-02-26
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Institute of Mathematical Statistics
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In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satis es 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 in uence 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 e cient; it does not require undersmoothing; and it is less sensitive to the rst-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 nite sample performance relative to competing methods.
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Empirical likelihood, Semiparametric inference, Highdimensional parameters, Wilks' phenomenon
Bibliographic citation
Bravo, F., Escanciano, J. C., & Van Keilegom, I. (2020). Two-step semiparametric empirical likelihood inference. The Annals of Statistics, 48 (1), pp. 1-26. https://doi.org/10.1214/18-aos1788