Singular gauss‐markov models
作者:
P. Scobey,
期刊:
Canadian Journal of Statistics
(WILEY Available online 1975)
卷期:
Volume 3,
issue 1
页码: 105-110
ISSN:0319-5724
年代: 1975
DOI:10.2307/3315102
出版商: Wiley‐Blackwell
关键词: Singular multivariate normal regression theory, sum of products matrix, Wishart distribution, Moore‐Penrose inverse
数据来源: WILEY
摘要:
AbstractFor the general linear model Y = X$sZ + e in which e has a singular dispersion matrix $sG2A, $sG>0, where A is n x n and singular, Mitra [2] considers the problem of testing F$sZ, where F is a known q x q matrix and claims that the sum of squares (SS) due to hypothesis is not distributed (as a x2variate with degrees of freedom (d. f.) equal to the rank of F) independent of the SS due to error, when a generalized inverse of A is chosen as (A + X'X)–. This claim does not hold if a pseudo‐inverse of A is taken to be (A + X'X)+where A+denotes the unique Moore‐Penrose inverse (MPI)
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