caa a22 4500 475826485 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1023/A:1004191713375 doi (NATIONALLICENCE)springer-10.1023/A:1004191713375 Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X2 Distribution [Elektronische Daten] [Satoshi Kuriki, Akimichi Takemura] Consider the test problem about matrix normal mean M with the null hypothesis M = O against the alternative that M is nonnegative definite. In our previous paper (Kuriki (1993, Ann. Statist., 21, 1379-1384)), the null distribution of the likelihood ratio statistic has been given in the form of a finite mixture of χ2 distributions referred to as X2 distribution. In this paper, we investigate differential-geometric structure such as second fundamental form and volume element of the boundary of the cone formed by real nonnegative definite matrices, and give a geometric derivation of this null distribution by virtue of the general theory on the X2 distribution for piecewise smooth convex cone alternatives developed by Takemura and Kuriki (1997, Ann. Statist., 25, 2368-2387). The Institute of Statistical Mathematics, 2000 One-sided test for covariance matrices nationallicence symmetric cone nationallicence mixed volume nationallicence second fundamental form nationallicence volume element nationallicence Kuriki Satoshi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan aut Takemura Akimichi Faculty of Economics, University of Tokyo, 7-3-1 Bunkyo-ku, 113-0033, Tokyo, Japan aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/1(2000-03-01), 1-14 0020-3157 52:1<1 2000 52 10463 https://doi.org/10.1023/A:1004191713375 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004191713375 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kuriki Satoshi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan aut NATIONALLICENCE 700 1- Takemura Akimichi Faculty of Economics, University of Tokyo, 7-3-1 Bunkyo-ku, 113-0033, Tokyo, Japan aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/1(2000-03-01), 1-14 0020-3157 52:1<1 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer