  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.
