Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix
Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix
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DOI：
10.1093/biomet/87.2.425
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发表时间：
2000-06-01
期刊：
影响因子：
2.7
通讯作者：
Pourahmadi, M
中科院分区：
文献类型：
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作者：
Pourahmadi, M
正定性约束是协方差矩阵建模中最棘手的绊脚石。Pourahmadi（1999）的无约束参数化模型使用协变量，以类似于广义线性模型中的平均建模的方式进行协方差建模。新的协方差参数具有作为回归系数的统计解释和对应于回归其前代响应的预测误差方差的估计。本文研究了观测值服从正态分布时广义线性模型协方差阵参数的极大似然估计及其相合性和渐近正态性。这些结果沿着的似然比测试和惩罚似然标准，如BIC模型和变量选择使用一个真实的数据集。
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.