Discussiones Mathematicae Probability and Statistics 20(2) (2000) 177-188

LIKELIHOOD AND PARAMETRIC HETEROSCEDASTICITY IN NORMAL CONNECTED LINEAR MODELS t

Joao Tiago Mexia and Pedro Corte Real

Universidade Nova de Lisboa, Departamento de Matemática
da Faculdade de Ciencias e Tecnologia,
Quinta da Torre, 2825 Monte de Caparica

e-mail: parcr@mail.fct.unl.pt

Abstract

A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.

Keywords: linear model, connected model, normal model, maximum likelihood estimators, score function, Newton-Raphson method.

1991 Mathematics Subject Classification: 62F10; 62J99.

References

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Received 19 April 1999
Revised 15 March 2000