Existence Of Maximum Likelihood Estimates Research Articles

On the existence and uniqueness of maximum likelihood estimates in polytomous response models

An ordered polytomous response model is defined. A geometric approach is used to derive the necessary and sufficient conditions for the existence of maximum likelihood estimates. The conditions are related to the idea of separating hyperplanes.

On the existence of maximum likelihood estimates in logistic regression models

SUMMARY The problems of existence, uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature (Haberman, 1974, Chapter 2; Wedderburn, 1976; Silvapulle, 1981). For multinomial logistic regression models, we prove existence theorems by considering the possible patterns of data points, which fall into three mutually exclusive and exhaustive categories: complete separation, quasicomplete separation and overlap. Our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables.

On the Existence of Maximum Likelihood Estimators for the Binomial Response Models

Summary Necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response (this includes Logit and Probit) models.

ON THE STRUCTURE OF THE LIKELIHOOD FUNCTION OF AUTOREGRESSIVE AND MOVING AVERAGE MODELS

Abstract. In finite order normal moving average models the maximum likelihood estimates always exist. For finite order normal autoregressive models sufficient conditions for the existence of maximum likelihood estimates is given. Some cases not satisfying the conditions are studied.