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.
Publié le : 1973-09-14
Classification:
Unimodal density,
the mode of a unimodal density,
upper and lower semicontinuity,
Levy metric,
convergence in the mean,
pointwise convergence,
compact and locally compact metric space,
weak topoloty and topology induced by the supremum-metric on families of probability measures,
asymptotic maximum likelihood estimates,
existence of measurable estimates,
strong consistency,
28A20,
62G05,
54A10,
54E45
@article{1176342509,
author = {Reiss, Rolf-Dieter},
title = {On the Measurability and Consistency of Maximum Likelihood Estimates for Unimodal Densities},
journal = {Ann. Statist.},
volume = {1},
number = {2},
year = {1973},
pages = { 888-901},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342509}
}
Reiss, Rolf-Dieter. On the Measurability and Consistency of Maximum Likelihood Estimates for Unimodal Densities. Ann. Statist., Tome 1 (1973) no. 2, pp. 888-901. http://gdmltest.u-ga.fr/item/1176342509/