Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach

Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach

We study statistical inference and robust solution methods for stochastic optimization prob-lems. We first develop an empirical likelihood framework for stochastic optimization. We showan empirical likelihood theory for Hadamard differentiable functionals with general f -divergencesand give conditions under which T (P ) = infx∈X EP [`(x; ξ)] is Hadamard differentiable. Noting<lb...

Generalized Likelihood Ratio Statistics

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood.

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated s...

Generalized Empirical Likelihood Estimators

In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a common structure, being members of a class of generalized empirical likelihood (GEL) estimators. We us...

On Generalized Empirical Likelihood Methods

We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with generalized empirical likelihood (GEL) approach. We treat the problems of existence and characterization of the divergence projections of probability measures on se...