期刊
BIOMETRIKA
卷 87, 期 2, 页码 425-435出版社
OXFORD UNIV PRESS
DOI: 10.1093/biomet/87.2.425
关键词
asymptotic normality; Cholesky decomposition; Fisher information; Newton-Raphson algorithm; unconstrained parameterisation; variable selection and diagnostics
The positive-definiteness constraint is the most awkward stumbling block in modelling the covariance -matrix. Pourahmadi's (1999) unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models. The new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors. In this paper, the maximum likelihood estimators of the parameters of a generalised linear model for the covariance matrix, their consistency and their asymptotic normality are studied when the observations are normally distributed. These results along with the likelihood ratio test and penalised likelihood criteria such as BIC for model and variable selection are illustrated using a real dataset.
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