APPLICATION OF THE COVARIANCE MATRIX OF
 SECOND-ORDER OF THE MAXIMUM LIKELIHOOD
 ESTIMATES IN THE INDUSTRY

Rosângela Getirana SANTANA[1]

Margareth Cizuka Toyama UDO1

Isolde Terezinha Santos PREVIDELLI1

Gauss Moutinho CORDEIRO [2]

§     ABSTRACT: Cordeiro and McCullagh (1991) and Cordeiro (2004) present simple matrix formulas to evaluate the biases of order (n-1) of the maximum likelihood estimates in generalized linear models and the covariance matrix of these estimates up to order n-2, respectively. However, these formulas had still not been explored in a practical context and, with this objective, we analyzed a cellulose data set through a gamma model with logarithmic link function. The implementation of the formulas of the corrected estimates and the covariance matrix is simple and was made using the computational system SAS. Some simulations show the evidence that for small samples it is important to use the covariance matrix of the maximum likelihood estimates in generalized linear models up to order n-2.

§     KEYWORDS: Bias of the estimate; corrected covariance matrix; corrected estimate; information matrix; maximum likelihood estimate



[1] Departamento de Estatística, Universidade Estadual de Maringá -- UEM, CEP: 87020-900, Maringá, PR, Brasil. E-mail: rgsantana@uem.br / mctudo@uem.br / itsprevidelli@uem.br

[2] Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco -- UFRPE, CEP: 52171-900, Recife, PE, Brasil. E-mail: gauss@deinfo.ufrpe.br