Adaptive confidence region for the direction in semiparametric regressions

Gao-Rong Li, Li-Ping Zhu and Li-Xing Zhu

Journal of Multivariate Analysis, 2010, vol. 101, issue 6, 1364-1377

Abstract: In this paper we aim to construct adaptive confidence region for the direction of [xi] in semiparametric models of the form Y=G([xi]TX,[epsilon]) where G([dot operator]) is an unknown link function, [epsilon] is an independent error, and [xi] is a pnx1 vector. To recover the direction of [xi], 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 [xi], 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.

Keywords: Confidence; region; Inverse; regression; Empirical; likelihood; Semiparametric; regressions; Single-index; models (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00032-1
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:101:y:2010:i:6:p:1364-1377

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().