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Covariance matrix estimation of the maximum likelihood estimator in multivariate clusterwise linear regression

机译：多变量群集线性回归中最大似然估计的协方差矩阵

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摘要

The expectation-maximisation algorithm is employed to perform maximum likelihood estimation in a wide range of situations, including regression analysis based on clusterwise regression models. A disadvantage of using this algorithm is that it is unable to provide an assessment of the sample variability of the maximum likelihood estimator. This inability is a consequence of the fact that the algorithm does not require deriving an analytical expression for the Hessian matrix, thus preventing from a direct evaluation of the asymptotic covariance matrix of the estimator. A solution to this problem when performing linear regression analysis through a multivariate Gaussian clusterwise regression model is developed. Two estimators of the asymptotic covariance matrix of the maximum likelihood estimator are proposed. In practical applications their use makes it possible to avoid resorting to bootstrap techniques and general purpose mathematical optimisers. The performances of these estimators are evaluated in analysing small simulated and real datasets; the obtained results illustrate their usefulness and effectiveness in practical applications. From a theoretical point of view, under suitable conditions, the proposed estimators are shown to be consistent.
机译：期望最大化算法用于在各种情况下执行最大似然估计，包括基于CompleSWOSE回归模型的回归分析。使用该算法的缺点是它无法提供最大似然估计器的样本变异性的评估。这种无法实现的结果是，算法不需要导出Hessian矩阵的分析表达，从而防止估计器的渐近协方差矩阵的直接评估。开发了通过开发通过多变量高斯群集回归模型执行线性回归分析的解决方案。提出了两种渐近协方差矩阵的两个估计值。在实际应用中，他们的用途使得可以避免诉诸于引导技术和通用数学优化器。在分析小型模拟和实际数据集时评估这些估计器的性能;所得结果说明了实际应用中的有用性和有效性。从理论的角度来看，在合适的条件下，所提出的估算器被证明是一致的。

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