Name: KURIKI

Firstname: Satoshi

Title: Associate Professor, Dr.

Institution: Institute of Statistical Mathematics

Street: 4-6-7 Minami-azabu

City: Minato-ku, Tokyo

Zip-Code: 106-8569

Country: JAPAN

Phone: +81-3-5421-8725

Fax: +81-3-5421-8796

Email: kuriki@ism.ac.jp

Authors: Satoshi KURIKI

Title: Limiting null distribution of the Jones-Sibson projection pursuit index and its approximation by the tube formula

Abstract: The projection pursuit index defined by a sum of squares of third and fourth sample cumulants is known as Jones and Sibson (1987)`s index.

Limiting distribution of the Jones-Sibson index under the null hypothesis that the population is multivariate normal is shown to be the maximum of a Gaussian random field with a finite Karhunen-Lo\`eve expansion.

An approximate upper tail probability of the maximum is obtained by the tube method, that is, the method approximating the distribution of maximum of a Gaussian random field by evaluating the volume of a tube region around the index manifold.