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3 Discussiones Mathematicae Probability and Statistics

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F-tests for generalized linear hypotheses in subnormal models

100%

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.

Likelihood and parametric heteroscedasticity in normal connected linear models

100%

Mexia J. , Real P.

Discussiones Mathematicae Probability and Statistics

2000

tom 20

nr 2

177-188

A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.

Exact distribution for the generalized F tests

80%

Fonseca M. , Mexia J. , Zmyślony R.

Discussiones Mathematicae Probability and Statistics

2002

tom 22

nr 1-2

37-51

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 the p-values whenever they are available.