Sankhya: The Indian Journal of Statistics
1972, Volume 34, Series B, Pt. 4, pp. 369--378
SOME RECENT RESULTS IN LINEAR ESTIMATION
C. RADHAKRISNA RAO, Indian Statistical Institute
SUMMARY. Some recent work of the author on 'Unified Theory of Linear
Estimation' is described. The general Gauss-Markov (GGM) model
$(Y, X\beta, \sigma^2V)$ is considered, where
$V=E[(Y-X\beta)(Y-X\beta)^\prime]$ is possibly singular and $X$
possibly deficient in rank. Aitken's procedure of least squares is
not applicable when $V$ is singular. The object of this paper is
to lay down procedures which are valid in all situations and which
do not require prior examination of the ranks of $V$ and $X$. Two
unified methods are suggested. One is a numerical approach called
the Inverse Partitioned Matrix (IPM)method. Another is an analogue
of the least square theory, called the Unified Least Squares (ULS)
It has been pointed out that singularity of $V$ imposes some restriction on the parameter $\beta$, which have to be taken into account in constructing unbiased estimators.
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