由选择分布产生的判别函数：理论与模拟
Discriminant functions arising from selection distributions: theory and simulation
摘要：
数据的正态性假设在统计分析领域中一直受到重视。然而，在许多实际情况下，这种假设显然是不现实的。最近有人建议，使用偏度/形状参数索引的分布在不同应用的建模中产生更大的灵活性。因此，结果显示了这些问题的更现实的解释。由于这些原因，本文的目的是调查的影响，通过类的多元扩展斜椭圆分布的判别函数方法的推广，详细研究多元扩展斜正态的情况下，并开发一个二次近似函数的分布家庭。一个模拟研究报告，以评估所提出的分类规则的充分性以及性能的期望最大化算法估计模型参数。
英文摘要：
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of distributions indexed by skewness/shape parameters produce more exibility in the modelling of different applications. Consequently, the results show a more realistic interpretation for these problems. For these reasons, the aim of this paper is to investigate the effects of the generalisation of a discrimination function method through the class of multivariate extended skew-elliptical distributions, study in detail the multivariate extended skew-normal case and develop a quadratic approximation function for this family of distributions. A simulation study is reported to evaluate the adequacy of the proposed classification rule as well as the performance of the EM algorithm to estimate the model parameters.
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