Adaptive confidence region for the direction in semiparametric regressions

Gao Rong Li, Li Ping Zhu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)1364-1377
Number of pages14
JournalJournal of Multivariate Analysis
Issue number6
Publication statusPublished - 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


Dive into the research topics of 'Adaptive confidence region for the direction in semiparametric regressions'. Together they form a unique fingerprint.

Cite this