Singular gauss‐markov models
P. Scobey · Canadian Journal of Statistics · 1975
Abstract For 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 x2 variate 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) of A.