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July, 1976 Gauss-Markov Estimation for Multivariate Linear Models with Missing Observations
Hilmar Drygas
Ann. Statist. 4(4): 779-787 (July, 1976). DOI: 10.1214/aos/1176343551


In this note we discuss multivariate linear models from the coordinate-free point of view, as earlier done by Eaton (1970). We generalize the result of Eaton by allowing for missing observations. This leads to models of the kind $EY \in L, Cov Y \in\{P(I \otimes \sum)P'\}$ where $P$ is a diagonal mapping. The paper starts by deriving the conditions for existence of Gauss-Markov estimators (GME) of $EY$ in models where the covariance-mappings are not necessarily nonsingular. These conditions are then applied to the above models if $\Sigma$ runs either over all PSD-mappings or over all diagonal PSD-mappings. In the latter case $L$ must be of the form $L = L_1 \times \cdots \times L_p$ while in the general case some further conditions on the $L_i$ must be met. (If $P = I$, then $L_i = L_j$ must hold for all $i, j$; this is equivalent to the result obtained by Eaton). Examples show that these conditions are satisfied only under rather exceptional conditions.


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Hilmar Drygas. "Gauss-Markov Estimation for Multivariate Linear Models with Missing Observations." Ann. Statist. 4 (4) 779 - 787, July, 1976.


Published: July, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0336.62052
MathSciNet: MR411060
Digital Object Identifier: 10.1214/aos/1176343551

Primary: 62F10
Secondary: 62J05

Keywords: Gauss-Markov estimation , linear models , missing observations , multivariate statistics , regression analysis

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 4 • July, 1976
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