IJPAM: Volume 32, No. 4 (2006)

STRONG CONSISTENCY OF THE MAXIMUM LIKELIHOOD
ESTIMATOR IN EXPONENTIAL FAMILY
NONLINEAR MODELS

Tian Xia$^1$, Xue-Ren Wang$^2$, Yan Hu$^3$, Xue-Jun Jiang$^4$
$^{1,2,4}$Department of Statistics
Yunnan University
Kunming, 650091, P.R. CHINA
$^1$e-mails: xiatian718@hotmail.com, xiatian403@yahoo.com.cn
$^2$e-mail: wangxr_34@hotmail.com
$^3$Department of Basic Studies
Vocational and Technical College
Anhui University
Hefei, 230011, P.R. CHINA


Abstract.This paper proposes the condition of eigenvalue, which is weaker than the corresponding condition in literature, and some other regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of the maximum likelihood estimator (MLE) in exponential family nonlinear models (EFNM). Our results may be regarded as an essential improvement comparing to the relevant results in literature.

Received: October 13, 2005

AMS Subject Classification: 62F12, 62J12

Key Words and Phrases: exponential family nonlinear models, strong consistency, maximum likelihood estimator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 4