A test for the equality of the direction parameters in a sample from the N-dimensional hyperboloid distribution

✍ Scribed by Muriel Casalis; Hélène Massam

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 194 KB
• Volume: 74
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(98)00097-4

✦ Synopsis

The problem considered in this paper is that of testing the equality of the direction parameters 1; : : : ; n for a sample (X1; : : : ; Xn) of independent variables Xi in R N having the N -dimensional hyperboloid distribution with parameters i . The N -dimensional hyperboloid distribution arises naturally when we consider a Wishart random variable Y on N = {(y0; : : : ; yN-1); y0¿0; y 2 0 -y 2 1 -• • • -y 2 N -1 ¿0} and condition on Y being on the unit hyperboloid H1 = {(y0; : : : ; yN-1); y0¿0; y 2 0 -y 2 1 -• • • -y 2 N -1 = 1}. The test for the equality of 1; : : : ; n is decomposed into a sequence of nested testing problems Hj+1; 0 : 1 = • • • = j = j+1 vs: Hj+1;a : 1 = • • • = j = j+1;

for j = 1; : : : ; n -1. The test statistic is the deviance Dj for testing Hj+1; 0 vs. Hj+1;a. The conditional density of Dj is given in Theorem 3.4.