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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...

Exponential regression

Lubomír Kubáček, Ludmila Kubáčková, Eva Tesaříková (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Extensions of the Frisch-Waugh-Lovell Theorem

Jürgen Groß, Simo Puntanen (2005)

Discussiones Mathematicae Probability and Statistics

In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.

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

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.

Factorial experimental designs and generalized linear models.

Simplice Dossou-Gbété, Walter Tinsson (2005)

SORT

This paper deals with experimental designs adapted to a generalized linear model. We introduce a special link function for which the orthogonality of design matrix obtained under Gaussian assumption is preserved. We investigate by simulation some of its properties.

Fitting a linear regression model by combining least squares and least absolute value estimation.

Sira Allende, Carlos Bouza, Isidro Romero (1995)

Qüestiió

Robust estimation of the multiple regression is modeled by using a convex combination of Least Squares and Least Absolute Value criterions. A Bicriterion Parametric algorithm is developed for computing the corresponding estimates. The proposed procedure should be specially useful when outliers are expected. Its behavior is analyzed using some examples.

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...

Gaussian model selection

Lucien Birgé, Pascal Massart (2001)

Journal of the European Mathematical Society

Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...

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...

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