380 – New Frontiers in Empirical Likelihood
An Easy Empirical Likelihood Approach to Efficient Estimation in Models with Side Information
Fei Tan
Indiana University-Purdue University Indianapolis
Hanxiang Peng
Indiana University-Purdue University Indianapolis
In this article, we construct semiparametrically efficient estimates in a nonparametric model with side information which can be described by expectation equations of some known functions. These estimates are given by easy maximum empirical likelihood estimates (MELEs) of the model that can found as solutions to certain estimating equations, which extend those of Qin and Lawless (1994) for MELEs from smooth estimating functions to discontinuous ones. In comparison with the usual MELEs, these are computationally fast and mathematically tractable. We calculate their computational complexities and derive easy MELEs for some problems of which the usual MELEs are difficult or even unable to be obtained. We give asymptotic normality and efficiency for MELEs in general M-estimation models which allow for discontinuous criterion and estimating functions. We also derive the MELEs for differentiable statistical functionals, von-Mises functionals, L-estimators, and U-statistics. Besides, we present several examples about side information.