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.
Original language | English |
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Pages (from-to) | 1364-1377 |
Number of pages | 14 |
Journal | Journal of Multivariate Analysis |
Volume | 101 |
Issue number | 6 |
DOIs | |
Publication status | Published - Jul 2010 |
Scopus Subject Areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty
User-Defined Keywords
- Confidence region
- Empirical likelihood
- Inverse regression
- Semiparametric regressions
- Single-index models