Displaying similar documents to “Selective generalized F tests”

Generalized F tests and selective generalized F tests for orthogonal and associated mixed models

Célia Nunes, Iola Pinto, João Tiago Mexia (2008)

Discussiones Mathematicae Probability and Statistics

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The statistics of generalized F tests are quotients of linear combinations of independent chi-squares. Given a parameter, θ, for which we have a quadratic unbiased estimator, θ̃, the test statistic, for the hypothesis of nullity of that parameter, is the quotient of the positive part by the negative part of such estimator. Using generalized polar coordinates it is possible to obtain selective generalized F tests which are especially powerful for selected families of alternatives. We...

F-tests for generalized linear hypotheses in subnormal models

Joao Tiago Mexia, Gerberto Carvalho Dias (2001)

Discussiones Mathematicae Probability and Statistics

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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...

On testing variance components in unbalanced mixed linear model

Lýdia Širková, Viktor Witkovský (2001)

Applications of Mathematics

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The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.

Tests of independence of normal random variables with known and unknown variance ratio

Edward Gąsiorek, Andrzej Michalski, Roman Zmyślony (2000)

Discussiones Mathematicae Probability and Statistics

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In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence...

Stable hypothesis for mixed models with balanced cross-nesting

Dário Ferreira, João Tiago Mexia, Sandra Saraiva Ferreira (2005)

Discussiones Mathematicae Probability and Statistics

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Stable hypothesis are hypothesis that may refer either for the fixed part or for the random part of the model. We will consider such hypothesis for models with balanced cross-nesting. Generalized F tests will be derived. It will be shown how to use Monte-Carlo methods to evaluate p-values for those tests.

F and selective F tests with balanced cross-nesting and associated models

Célia Nunes, Iola Pinto, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

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F tests and selective F tests for fixed effects part of balanced models with cross-nesting are derived. The effects of perturbations in the numerator and denominator of the F statistics are considered.

Selective F tests for sub-normal models

Célia Maria Pinto Nunes, João Tiago Mexia (2003)

Discussiones Mathematicae Probability and Statistics

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F tests that are specially powerful for selected alternatives are built for sub-normal models. In these models the observation vector is the sum of a vector that stands for what is measured with a normal error vector, both vectors being independent. The results now presented generalize the treatment given by Dias (1994) for normal fixed-effects models, and consider the testing of hypothesis on the ordering of mean values and components.