On Estimated Projection Pursuit-Type Crámer–von Mises Statistics

✍ Scribed by Li-Xing Zhu; Kai-Tai Fang; M Ishaq Bhatti

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 319 KB
• Volume: 63
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1997.1673

✦ Synopsis

This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Cra mer Von Mises-type test statistics are constructed using projection pursuit technique. Some interested properties of the test statistics, like asymptotics, bootstrap approximations, and the tail behavior of the limits of test statistics are investigated. For computational reasons, an approximation via the number theoretic method to the extreme value and the integral on a super sphere surface is considered. 1997 Academic Press Ä n are i.i.d. sample from G( } ). A statistical problem addressed in this article is how to test G( } ) which is a member of a known family of probability measures with unknown parameter, that is, how to test G(})=P % (} ), article no. MV971673 1 0047-259XÂ97 25.00