Title: Associate Professor, Dr.
Institution: Institute of Statistical Mathematics
Street: 4-6-7 Minami-azabu
City: Minato-ku, Tokyo
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.