Statistics and Its Interface

Volume 5 (2012)

Number 3

On the Mahalanobis-distance based penalized empirical likelihood method in high dimensions

Pages: 331 – 338

DOI: https://dx.doi.org/10.4310/SII.2012.v5.n3.a5

Authors

S. N. Lahiri (Department of Statistics, Texas A&M University, College Station, Tx., U.S.A.)

S. Mukhopadhyay (Department of Statistics, Texas A&M University, College Station, Tx., U.S.A.)

Abstract

In this paper, we consider the penalized empirical likelihood (PEL) method of Bartolucci (2007) for inference on the population mean which is a modification of the standard empirical likelihood and employs a penalty based on the Mahalanobis-distance. We derive the asymptotic distributions of the PEL ratio statistic when the dimension of the observations increases with the sample size. Finite sample properties of the method are investigated through a small simulation study.

Keywords

asymptotic null distribution, empirical likelihood, high dimension, regularization, simultaneous tests

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Published 14 September 2012