Empirical Envelope Mle and Lr Tests
نویسنده
چکیده
We study in this paper some nonparametric inference problems where the nonparametric maximum likelihood estimator (NPMLE) are not well defined. However, if we enlarge the parameter space, the NPMLE will be well defined. We propose to gradually shrink the enlarged parameter space by placing more and more restrictions on the parameter space, producing a sequence of (envelope) estimators. The approach is a counter part of the sieve MLE (Grenander, 1981). Several different problems where this method can be applied effectively are discussed. The detailed treatment of 2-sample location problem is presented, including a Wilks type theorem for the empirical envelope likelihood ratio statistic and the asymptotic distribution of the empirical envelope MLE of location.
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