Open Access
October 2012 A penalized empirical likelihood method in high dimensions
Soumendra N. Lahiri, Subhadeep Mukhopadhyay
Ann. Statist. 40(5): 2511-2540 (October 2012). DOI: 10.1214/12-AOS1040


This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure, and it is typically different from the usual chi-squared limit of the empirical likelihood ratio statistic in the fixed and finite dimensional case. A unified subsampling based calibration is proposed, and its validity is established in all three cases, (i)–(iii). Finite sample properties of the method are investigated through a simulation study.


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Soumendra N. Lahiri. Subhadeep Mukhopadhyay. "A penalized empirical likelihood method in high dimensions." Ann. Statist. 40 (5) 2511 - 2540, October 2012.


Published: October 2012
First available in Project Euclid: 4 February 2013

zbMATH: 1373.62132
MathSciNet: MR2979212
Digital Object Identifier: 10.1214/12-AOS1040

Primary: 62G09
Secondary: 62E20 , 62G20

Keywords: asymptotic distribution , long-range dependence , regularization , Rosenblatt process , simultaneous tests , subsampling , Wiener–Itô integral

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 5 • October 2012
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