TWO-STEP SEMIPARAMETRIC EMPIRICAL LIKELIHOOD INFERENCE

• 成果类型: Article
• 署名作者: Bravo, Francesco; Carlos Escanciano, Juan; Van Keilegom, Ingrid
• 署名单位: University of York - UK; Universidad Carlos III de Madrid; KU Leuven
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1788
• 发表日期: 2020
• 页码: 1-26
• 关键词: estimating equations; efficient estimation; regression-analysis; confidence-regions; linear-regression; missing response; models; ratio; tests; imputation

摘要

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.