A NOTE ON NONREGULAR LIKELIHOOD FUNCTIONS IN HETEROSCEDASTIC REGRESSION-MODELS

Authors
CRISP A BURRIDGE J
Citation
A. Crisp et J. Burridge, A NOTE ON NONREGULAR LIKELIHOOD FUNCTIONS IN HETEROSCEDASTIC REGRESSION-MODELS, Biometrika, 81(3), 1994, pp. 585-587
Citations number
6
Categorie Soggetti
Mathematical Methods, Biology & Medicine","Statistic & Probability
Journal title
Biometrika → ACNP
ISSN journal
00063444
Volume
81
Issue
3
Year of publication
1994
Pages
585 - 587
Database
ISI
SICI code
0006-3444(1994)81:3<585:ANONLF>2.0.ZU;2-2
Abstract
The existence of maximum likelihood estimates for a class of heterosce dastic regression models is considered. For a given dispersion functio n we show that, under a weak condition, the likelihood is singular at points corresponding to nonreplicated observations, causing unrestrict ed maximum likelihood estimation to break down, whilst for an alternat ive class of dispersion functions we obtain a much stronger linear ind ependence condition for the likelihood to be unbounded.