A Class of Uniform Tests for Goodness-of-Fit of the Multivariate $L_P$-Norm Spherical Distributions and the $L_P$-Norm Symmetric Distributions

• Activity Number: 399
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiajuan Liang*+
• Keywords: Goodness-of-fit ; $L_p$-norm spherical distribution ; $l_p$-norm symmetric distribution

Abstract

In this paper we employ the conditional probability integral transformation (CPIT) method to transform a $d$-dimensional sample from a population with either an $L_p$-norm spherical distribution or an $l_p$-norm symmetric distribution into a uniform sample in the unit interval $(0,\,1)$ or in the unit hypercube $[0,\,1]^{d-1}$ ($d\ge 2$). A class of existing uniform statistics are adopted to test the uniformity of the transformed sample. Monte Carlo studies are carried out to demonstrate the performance of the tests in controlling type I error rates and power against a selected group of alternative distributions. It is concluded that the proposed tests have satisfactory empirical performance and the CPIT method in this paper can serve as a general way to construct goodness-of-fit tests for many generalized multivariate distributions.