Empirical likelihood confidence regions in the single-index model with growing dimensions

Guangren Yang, Xia Cui, Sumin Hou

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

This paper investigates statistical inference for the single-index model when the number of predictors grows with sample size. Empirical likelihood method for constructing confidence region for the index vector, which does not require a multivariate non parametric smoothing, is employed. However, the classical empirical likelihood ratio for this model does not remain valid because plug-in estimation of an infinite-dimensional nuisance parameter causes a non negligible bias and the diverging number of parameters/predictors makes the limit not chi-squared any more. To solve these problems, we define an empirical likelihood ratio based on newly proposed weighted estimating equations and show that it is asymptotically normal. Also we find that different weights used in the weighted residuals require, for asymptotic normality, different diverging rate of the number of predictors. However, the rate n1/3, which is a possible fastest rate when there are no any other conditions assumed in the setting under study, is still attainable. A simulation study is carried out to assess the performance of our method.

Original languageEnglish (US)
Pages (from-to)7562-7579
Number of pages18
JournalCommunications in Statistics - Theory and Methods
Volume46
Issue number15
DOIs
StatePublished - Aug 3 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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