Changbao Wu
University of Waterloo

Empirical Likelihood Inference for a Common Mean in the Presence of Heteroscedasticity           

In this talk we address an old problem, inference for a common mean with data from several independent but nonhomogeneous samples, using the recently developed empirical likelihood (EL) method. For point estimation, we propose a maximum empirical likelihood (MEL) estimator and show that it is root-n consistent and is asymptotically optimal. For confidence intervals, we consider several EL based methods and show that all these intervals have approximately correct coverage probabilities under large samples. Finite sample performances of the MEL estimator and the EL based confidence intervals are evaluated through a simulation study. Our results indicate that overall the MEL estimator and the weighted EL confidence interval are superior alternatives to the existing methods. Possible extensions to combining information from samples with un-common means will also be discussed. This talk is primarily based on the joint work with Min Tsao of University of Victoria, which will appear in CJS in 2006.