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February, 1972 Existence and Consistency of Modified Minimum Contrast Estimates
D. Landers
Ann. Math. Statist. 43(1): 74-83 (February, 1972). DOI: 10.1214/aoms/1177692702


It is the purpose of this paper to explore the efficiency of a modified definition for maximum likelihood estimates which depends on the whole equivalence class of densities only and not--as in the classical case--on the particular choice of versions. We prove the existence of measurable maximum likelihood estimates in the new sense for compact metrizable families of probability measures without any continuity assumption for the densities. For appropriate families of probability measures the modified asymptotic maximum likelihood estimates are exactly the strongly consistent estimates. The paper uses Huber's concept of minimum contrast estimates which covers maximum likelihood estimates as a special case.


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D. Landers. "Existence and Consistency of Modified Minimum Contrast Estimates." Ann. Math. Statist. 43 (1) 74 - 83, February, 1972.


Published: February, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0238.62031
MathSciNet: MR311023
Digital Object Identifier: 10.1214/aoms/1177692702

Rights: Copyright © 1972 Institute of Mathematical Statistics


Vol.43 • No. 1 • February, 1972
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