Inferential Aspects of the Skew Exponential Power Distribution
Inferential Aspects of the Skew Exponential Power Distribution
复制标题
斜指数功率分布的推论
DOI：
10.1198/016214504000000359
复制
发表时间：
2004
影响因子：
3.7
通讯作者：
Anna Clara Monti
中科院分区：
文献类型：
--
作者：
T. DiCiccio;Anna Clara Monti
当对真实的数据的分析表明正态性假设不成立时，可以采用更灵活的模型来科普最普遍的正态性偏差。在这种情况下，偏指数幂（SEP）分布值得特别注意，因为它包含具有重尾和偏度的分布，它允许似然推断，并且它包括正态模型作为特殊情况。本文讨论SEP族参数的似然推断。特别地，得到了极大似然估计的信息矩阵，并对估计的有限样本性质进行了数值研究。特别注意的MLE和似然比统计的属性时，数据是从一个正常的分布，因为这种情况下是相关的使用SEP分布来检验正态性。SEP分布在稳健估计问题中的应用被认为是独立和相关的数据。在中度偏离正态分布下，SEP分布下获得的估计量优于基于正态分布的估计量，并与稳健估计量竞争;此外，SEP分布提供了具有指定分布的好处，例如非正态分布下可解释的位置和尺度参数。
When the analysis of real data indicates that normality assumptions are untenable, more flexible models that cope with the most prevalent deviations from normality can be adopted. In this context, the skew exponential power (SEP) distribution warrants special attention, because it encompasses distributions having both heavy tails and skewness, it allows likelihood inference, and it includes the normal model as a special case. This article concerns likelihood inference about the parameters of the SEP family. In particular, the information matrix of the maximum likelihood estimators (MLEs) is obtained and finite-sample properties of the estimators are investigated numerically. Special attention is given to the properties of the MLEs and likelihood ratio statistics when the data are drawn from a normal distribution, because this case is relevant for using the SEP distribution to test for normality. Application of the SEP distribution in robust estimation problems is considered for both independent and dependent data. Under moderate deviations from normality, estimators obtained under the SEP distribution are shown to outperform the normal-based estimators and to compete with robust estimators; furthermore, the SEP distribution offers the benefits of having a specified distribution, such as interpretable location and scale parameters under nonnormality.