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Biometrika Advance Access originally published online on August 8, 2009
Biometrika 2009 96(3):711-722; doi:10.1093/biomet/asp037
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© 2009 Biometrika Trust

Article

Effects of data dimension on empirical likelihood

Song Xi Chen

Department of Statistics, Iowa State University, Iowa 50011-1210, U.S.A. songchen{at}iastate.edu

Liang Peng

School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, U.S.A. peng{at}math.gatech.edu

Ying-Li Qin

Department of Statistics, Iowa State University, Iowa 50011-1210, U.S.A. qinyl{at}iastate.edu

Received for publication 1 July 2007. Revision received 1 November 2008.
  Abstract

We evaluate the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high-dimensional data under a general multivariate model. Data dimension and dependence among components of the multivariate random vector affect the empirical likelihood directly through the trace and the eigenvalues of the covariance matrix. The growth rates to infinity we obtain for the data dimension improve the rates of Hjort et al. (2008).

Key Words: Asymptotic normality • Data dimension • Empirical likelihood • High-dimensional data


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