Qiqing Yu, "The Necessary and Sufficient Condition for Consistency of the MLE," WSEAS Transactions on Systems, vol. 20, pp. 124-132, 2021, DOI:10.37394/23202.2021.20.14
Qiqing Yu. The Necessary and Sufficient Condition for Consistency of the MLE.
WSEAS Transactions on Systems. 2021;20:124-132. 10.37394/23202.2021.20.14
WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 20, 2021
The Necessary and Sufficient Condition for Consistency of the MLE
Author:
Abstract: 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.
Keywords:
Maximum likelihood estimator, consistency, Kullback-Leibler Inequality, parametric family, sufficient condition
Pages: 124-132 WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 20, 2021, Art. #14 DOI: 10.37394/23202.2021.20.14
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