Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values |
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Authors: | Wiktor Oktaba |
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Institution: | (1) Institute of Applied Mathematics, Department of Mathematical Statistics, Agricultural University, Akademicka 13, 20-934 Lublin, Poland |
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Abstract: | The aim of this paper is to characterize the Multivariate Gauss-Markoff model (MGM) as in (2.1) with singular covariance matrix and missing values. MGMDP2 model and completed MGMDP2Q model are obtained by three transformations D, P and Q (cf. (3.21)) of MGM. The unified theory of estimation (Rao, 1973) which is of interest with respect to MGM has been used.The characterization is reached by estimation of parameters: scalar 2 and linear combination
as in (4.8), (4.6), (4.7) as well as by the model of the form (5.1) (cf. Th. 5.1). Moreover, testing linear hypothesis in the available model MGMDP2 by test function F as in (6.3) and (6.4) is considered.It is known (Oktaba 1992) that ten quantities in models MGMDP2, and MGMDP2Q are identical (invariant). They permit to say that formulas for estimation and testing in both models are identical (Oktaba et al., 1988, Baksalary and Kala, 1981, Drygas, 1983).An algorithm and the UMGMBO program for calculations concerning estimation and testing in MGM have been presented by Oktaba and Osypiuk (1993). |
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Keywords: | multivariate Gauss-Markoff model missing value developed model available model completed model elementary transformation BLUE estimation testing consistency invariant |
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