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September, 1973 On the Measurability and Consistency of Maximum Likelihood Estimates for Unimodal Densities
Rolf-Dieter Reiss
Ann. Statist. 1(5): 888-901 (September, 1973). DOI: 10.1214/aos/1176342509

Abstract

This paper is concerned with maximum likelihood estimates for a large class of families of unimodal densities. The existence of measurable maximum likelihood estimates and the consistency of asymptotic maximum likelihood estimates are proved. By counterexamples it is shown that the conditions which are sufficient for consistency cannot be removed without compensation.

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Rolf-Dieter Reiss. "On the Measurability and Consistency of Maximum Likelihood Estimates for Unimodal Densities." Ann. Statist. 1 (5) 888 - 901, September, 1973. https://doi.org/10.1214/aos/1176342509

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0274.62028
MathSciNet: MR368286
Digital Object Identifier: 10.1214/aos/1176342509

Subjects:
Primary: 28A20
Secondary: 54A10 , 54E45 , 62G05

Keywords: asymptotic maximum likelihood estimates , compact and locally compact metric space , convergence in the mean , existence of measurable estimates , Levy metric , pointwise convergence , strong consistency , the mode of a unimodal density , Unimodal density , upper and lower semicontinuity , weak topoloty and topology induced by the supremum-metric on families of probability measures

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • September, 1973
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