An Estimator Based on Empirical Likelihood and Its Properties

Abstract

A nonparametric statistical method called the empirical likelihood (EL) is applied to estimation problems with side information. Since EL is formulated as the KL-divergence minimization, a variant called the exponential tilting (ET) is also discussed that employs the divergence of the opposite direction. Theoretical analyses of the methods show that they are almost the same in the asymptotic performance but different in an algorithmic difficulty. Some numerical experiments confirm the above analyses.