Projector operators in the multivariate Zyskind-Martin model |
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Authors: | Wiktor Oktaba Joanna Tarasinska |
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Institution: | (1) Institute of Applied Mathematics, Academy of Agriculture, Akademicka 13, 20-934 Lublin, Poland |
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Abstract: | Summary Two quadratic formsS
H andS
E for a testable hypothesis and for an error in the multivariate Zyskind-Martin model with singular covariance matrix are expressed
by means of projector operators. Thus the results for the multivariate standard model with identity covariance matrix given
by Humak (1977) and Christensen (1987, 1991) are generalized for the case of Zyskind-Martin model. Special cases of our results
are formulae forS
H andS
E in Aitken's (1935) model. In the case of general Gauss-Markoff modelS
H andS
E can also be expressed by means of projector operators for some subclasses of testable hypotheses. For these hypotheses, testing
in Gauss-Markoff model is equivalent to testing in a Zyskind-Martin model. |
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Keywords: | Multivariate standard model Aitken model Zyskind-Martin model projector operator with respect to seminorm g-inverse matrix testable hypothesis matrices of products for hypothesis and for error |
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