Empirical Envelope MLE for a Location Problem

Mai Zhou

Abstract:

We study in this paper the NPMLE of a location shift parameter in a 2-sample setting. The NPMLE of the location parameter do not exist in the original setup. But if we enlarge the parameter space, the NPMLE will exist. We propose to gradually shrink the enlarged parameter space by placing more and more restrictions on the parameter space, and producing a sequence of location estimators. The approach is the counter part of the sieve MLE estimator (Grenander, 1981). A Wilks type theorem for the empirical likelihood ratio statistic and the asymptotic distribution of the location estimator are provided.

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