A family of estimators for multivariate kurtosis in a nonnormal linear regression model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:98

Article

Yanagihara, Hirokazu

关键词: bias correction;    Hotelling's T-2 distribution;    Mahalanobis distance;    monotonic increasing function;    multivariate linear model;    nonnormality;    predicted residuals;    studentized residuals;    tuning parameter;   

DOI  :  10.1016/j.jmva.2005.05.015

来源: Elsevier

【 摘 要 】

In this paper, we propose anew estimator for a kurtosis in a multivariate nonnormal linear regression model. Usually, an estimator is constructed from an arithmetic mean of the second power of the squared sample Mahalanobis distances between observations and their estimated values. The estimator gives an underestimation and has a large bias, even if the sample size is not small. We replace this squared distance with a transformed squared norm of the Studentized residual using a monotonic increasing function. Our proposed estimator is defined by an arithmetic mean of the second power of these transformed squared norms with a correction term and a tuning parameter. The correction term adjusts our estimator to an unbiased estimator under normality, and the tuning parameter controls the sizes of the squared norms of the residuals. The family of our estimators includes estimators based on ordinary least squares and predicted residuals. We verify that the bias of our new estimator is smaller than usual by constructing numerical experiments. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free