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.

期望最大化算法用于在各种情况下执行最大似然估计，包括基于聚类回归模型的回归分析。使用该算法的一个缺点是它无法提供对最大似然估计器的样本变异性的评估。这种无能是由于以下事实的结果：该算法不需要导出Hessian矩阵的解析表达式，从而阻止了对估计器的渐近协方差矩阵的直接评估。开发了通过多元高斯聚类回归模型进行线性回归分析时解决此问题的方法。提出了最大似然估计的渐近协方差矩阵的两个估计。在实际应用中，使用它们可以避免采用自举技术和通用数学优化器。这些估计器的性能在分析小型模拟和真实数据集时得到评估；获得的结果说明了它们在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，拟议的估计量是一致的。