Penalized high-dimensional empirical likelihood

We propose penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters. Our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models. By using an appropriate penalty function, we showthat penalized empirical likelihood has the oracle property. That is, with probability tending to 1, penalized empirical likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. The advantage of penalized empirical likelihood as a nonparametric likelihood approach is illustrated by testing hypotheses and constructing confidence regions. Numerical simulations confirm our theoretical findings.