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This paper formulates a penalized empirical likelihood (PEL) method forinference on the population mean when the dimension of the observations maygrow faster than the sample size. Asymptotic distributions of the PEL ratiostatistic is derived under different component-wise dependence structures ofthe observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii)short-range dependence. It follows that the limit distribution of the proposedPEL ratio statistic can vary widely depending on the correlation structure, andit is typically different from the usual chi-squared limit of the empiricallikelihood ratio statistic in the fixed and finite dimensional case. A unifiedsubsampling based calibration is proposed, and its validity is established inall three cases, (i)-(iii). Finite sample properties of the method areinvestigated through a simulation study.

A penalized empirical likelihood method in high dimensions