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Estimators and tests for variance components in cross nested orthogonal designs

Miguel Fonseca, João Tiago Mexia, Roman Zmyślony (2003)

Discussiones Mathematicae Probability and Statistics

Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.

Exact distribution for the generalized F tests

Miguel Fonseca, Joao Tiago Mexia, Roman Zmyślony (2002)

Discussiones Mathematicae Probability and Statistics

Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate...

F-tests for generalized linear hypotheses in subnormal models

Joao Tiago Mexia, Gerberto Carvalho Dias (2001)

Discussiones Mathematicae Probability and Statistics

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...

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

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 build both classes...

Graphs, topologies and simple games.

Jesús Mario Bilbao (2000)

Qüestiió

We study the existence of connected coalitions in a simple game restricted by a partial order. First, we define a topology compatible with the partial order in the set of players. Second, we prove some properties of the covering and comparability graphs of a finite poset. Finally, we analize the core and obtain sufficient conditions for the existence of winning coalitions such that contains dominant players in simple games restricted by the connected subspaces of a finite topological space.

Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation

Pavel Strachota (2009)

Kybernetika

Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the Allen–Cahn...

Intrinsic priors for hypothesis testing in normal regression models.

Elías Moreno, F. Javier Girón, Francisco Torres (2003)

RACSAM

Testing that some regression coefficients are equal to zero is an important problem in many applications. Homoscedasticity is not necessarily a realistic condition in this setting and, as a consequence, no frequentist test there exist. Approximate tests have been proposed. In this paper a Bayesian analysis of this problem is carried out, from a default Bayesian model choice perspective. Explicit expressions for intrinsic priors are provided, and it is shown that the corresponding Bayes factor is...

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