http://dx.doi.org/10.1016/j.jmva.2010.02.002">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Adaptive confidence region for the direction in semiparametric regressions

Language

English

Abstract

In this paper we aim to construct adaptive confidence region for the direction of ξ in semiparametric models of the form Y = G (ξT X, ε) where G ({dot operator}) is an unknown link function, ε is an independent error, and ξ is a pn × 1 vector. To recover the direction of ξ, we first propose an inverse regression approach regardless of the link function G ({dot operator}); to construct a data-driven confidence region for the direction of ξ, we implement the empirical likelihood method. Unlike many existing literature, we need not estimate the link function G ({dot operator}) or its derivative. When pn remains fixed, the empirical likelihood ratio without bias correlation can be asymptotically standard chi-square. Moreover, the asymptotic normality of the empirical likelihood ratio holds true even when the dimension pn follows the rate of pn = o (n1 / 4) where n is the sample size. Simulation studies are carried out to assess the performance of our proposal, and a real data set is analyzed for further illustration. © 2010 Elsevier Inc. All rights reserved.

Keywords

Confidence region, Empirical likelihood, Inverse regression, Semiparametric regressions, Single-index models

Publication Date

2010

Source Publication Title

Journal of Multivariate Analysis

Volume

101

Issue

6

Start Page

1364

End Page

1377

Publisher

Elservier

ISSN (print)

0047259X

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