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Orthogonal models: Algebraic structure and explicit estimators for estimable vectors

100%

Pereira A., Fonseca M., Mexia J.

Discussiones Mathematicae Probability and Statistics

2015

tom 35

nr 1-2

29-44

We study the algebraic structure of orthogonal models thus of mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known pairwise orthogonal projection matrices, POOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expression for the LSE of these models.

F-tests for generalized linear hypotheses in subnormal models

86%

Mexia J., Dias G.

Discussiones Mathematicae Probability and Statistics

2001

tom 21

nr 1

49-62

When the measurement errors may be assumed to be normal and independent from what is measured a subnormal model may be used. We define a linear and generalized linear hypotheses for these models, and derive F-tests for them. These tests are shown to be UMP for linear hypotheses as well as strictly unbiased and strongly consistent for these hypotheses. It is also shown that the F-tests are invariant for regular transformations, possess structural stability and are almost strongly consistent for generalized linear hypothesis. An application to a mixed model studied by Michalskyi and Zmyślony is shown.

Ograniczanie wyników

2 Discussiones Mathematicae Probability and Statistics

2 Mexia J.

1 Dias G.

1 Fonseca M.

1 Pereira A.

1 2015

1 2001

Wyniki wyszukiwania

Orthogonal models: Algebraic structure and explicit estimators for estimable vectors

F-tests for generalized linear hypotheses in subnormal models