caa a22 4500 477092268 CHVBK 20180405111518.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF02589096 doi (NATIONALLICENCE)springer-10.1007/BF02589096 Projector operators in the multivariate Zyskind-Martin model [Elektronische Daten] [Wiktor Oktaba, Joanna Tarasinska] 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. Società Italiana di Statistica, 1996 Multivariate standard model nationallicence Aitken model nationallicence Zyskind-Martin model nationallicence projector operator with respect to seminorm nationallicence g-inverse matrix nationallicence testable hypothesis nationallicence matrices of products for hypothesis and for error nationallicence Oktaba Wiktor Institute of Applied Mathematics, Academy of Agriculture, Akademicka 13, 20-934, Lublin, Poland aut Tarasinska Joanna Institute of Applied Mathematics, Academy of Agriculture, Akademicka 13, 20-934, Lublin, Poland aut Journal of the Italian Statistical Society Springer-Verlag 5/3(1996-12-01), 361-367 1121-9130 5:3<361 1996 5 10260 https://doi.org/10.1007/BF02589096 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02589096 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Oktaba Wiktor Institute of Applied Mathematics, Academy of Agriculture, Akademicka 13, 20-934, Lublin, Poland aut NATIONALLICENCE 700 1- Tarasinska Joanna Institute of Applied Mathematics, Academy of Agriculture, Akademicka 13, 20-934, Lublin, Poland aut NATIONALLICENCE 773 0- Journal of the Italian Statistical Society Springer-Verlag 5/3(1996-12-01), 361-367 1121-9130 5:3<361 1996 5 10260 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer