Necessary and Sufficient Conditions for MINQU-Estimation of Heteroskedastic Variances in Linear Models
Parthasaradhi Mallela · Journal of the American Statistical Association · 1972
Let y = Xβ+e be a Gauss-Markoff linear model such that E(e) = 0 and D(e), the dispersion matrix of the error vector, is a diagonal matrix whose ith diagonal element is σ2 i, the variance of the ith observation yi. Rao has recently brought out two sets of sufficient conditions (on X) for the MINQU-estimability of all the heteroskedastic variances. In this note, we have derived a set of necessary and sufficient conditions for the same purpose.