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In this paper we aim to construct adaptive confidence region for the direction of xi in semiparametric models of the form Y = G(xi(T) X, epsilon) where G(center dot) is an unknown link function, E is an independent error, and xi is a p(n) x 1 vector. To recover the direction of xi, we first propose an inverse regression approach regardless of the link function G(center dot); 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(center dot) or its derivative. When p(n) 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 p(n) follows the rate of p(n) = o(n(1/4)) 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. (C) 2010 Elsevier Inc. All rights reserved.
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JOURNAL OF MULTIVARIATE ANALYSIS
ISSN: 0047-259X
Year: 2010
Issue: 6
Volume: 101
Page: 1364-1377
1 . 6 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 3
SCOPUS Cited Count: 3
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 7
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