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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...

Generalized F tests in models with random perturbations: the gamma case

Célia Maria Pinto Nunes, Sandra Maria Bargão Saraiva Ferreira, Dário Jorge da Conceição Ferreira (2009)

Discussiones Mathematicae Probability and Statistics

Generalized F tests were introduced for linear models by Michalski and Zmyślony (1996, 1999). When the observations are taken in not perfectly standardized conditions the F tests have generalized F distributions with random non-centrality parameters, see Nunes and Mexia (2006). We now study the case of nearly normal perturbations leading to Gamma distributed non-centrality parameters.

Generalized length biased distributions

Giri S. Lingappaiah (1988)

Aplikace matematiky

Generalized length biased distribution is defined as h ( x ) = φ r ( x ) f ( x ) , x > 0 , where f ( x ) is a probability density function, φ r ( x ) is a polynomial of degree r , that is, φ r ( x ) = a 1 ( x / μ 1 ' ) + ... + a r ( x r / μ r ' ) , with a i > 0 , i = 1 , ... , r , a 1 + ... + a r = 1 , μ i ' = E ( x i ) for f ( x ) , i = 1 , 2 ... , r . If r = 1 , we have the simple length biased distribution of Gupta and Keating [1]. First, characterizations of exponential, uniform and beta distributions are given in terms of simple length biased distributions. Next, for the case of generalized distribution, the distribution of the sum of n independent variables is put in the closed form when f ( x ) ...

Geometría estadística en los espacios de distancia y secuencia: dos aplicaciones.

Eladio Barrio, Celia Buades, Andrés Moya (1992)

Qüestiió

La Geometría estadística es un método complementario a los desarrollados hasta el momento para la inferencia y evaluación de las relaciones filogenéticas entre entidades emparentadas, y que permite decidir si la estructura filogenética obtenida tiene una configuración de árbol, de estrella o de red.El objetivo de este trabajo consiste en poner de manifiesto que, si bien la geometría estadística puede ayudar a decidir entre grandes topologías, no puede decidir entre tipos específicos de topologías....

Global information in statistical experiments and consistency of likelihood-based estimates and tests

Igor Vajda (1998)

Kybernetika

In the framework of standard model of asymptotic statistics we introduce a global information in the statistical experiment about the occurrence of the true parameter in a given set. Basic properties of this information are established, including relations to the Kullback and Fisher information. Its applicability in point estimation and testing statistical hypotheses is demonstrated.

Global robust output regulation of a class of nonlinear systems with nonlinear exosystems

Yuan Jiang, Ke Lu, Jiyang Dai (2020)

Kybernetika

An adaptive output regulation design method is proposed for a class of output feedback systems with nonlinear exosystem and unknown parameters. A new nonlinear internal model approach is developed in the present study that successfully converts the global robust output regulation problem into a robust adaptive stabilization problem for the augmented system. Moreover, an output feedback controller is achieved based on a type of state filter which is designed for the transformed augmented system....

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