首页|The Necessary And Sufficient Condition For Consistency Of The MLE
The Necessary And Sufficient Condition For Consistency Of The MLE
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NSTL
Suppose that the observations are i.i.d. from a density f(·; θ), where θ is an identifiable parameter. One expects that the maximum likelihood estimator of θ is consistent. But its consistency proof is non-trivial and various sufficient conditions have been proposed (see, e.g., the classical statistics textbooks). All these sufficient conditions require f(x; θ) being somewhat upper semi-continuous (in θ), with various smoothness conditions or conditions needed for the dominated convergence theorem. We study the sufficient and necessary condition.
Maximum likelihood estimatorConsistencyKullback-Leibler inequalityParametric familySufficient condition
QIQING YU
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Department of Mathematical Sciences State University of New York
NSTL
