A Penalized Empirical Likelihood Method in High Dimensions

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Subhadeep Mukhopadhyay*+ and Soumendra Nath Lahiri
• Companies: Texas A&M University and Texas A&M University
• Keywords: penalized empirical likelihood ; asymptotic distribution ; correlation structure ; subsampling

Abstract

In this paper, we formulate a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations become unbounded with the sample size. We derive the asymptotic distribution of the PEL ratio statistic. It is shown that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure of different components of the observation, and it is typically different from the usual chi-squared limit of the empirical likelihood ratio statistic in the finite dimensional case. We propose a subsampling method for approximating the limit distribution in a unified manner and establish its validity. Finite sample properties of the method are investigated through a simulation study. Further, we also illustrate the method in a real data example involving gene expression data.