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Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models

Christian Genest, Bruno Rémillard (2008)

Annales de l'I.H.P. Probabilités et statistiques

In testing that a given distribution Pbelongs to a parameterized family 𝒫 , one is often led to compare a nonparametric estimateAn of some functional A of P with an element Aθn corresponding to an estimate θn of θ. In many cases, the asymptotic distribution of goodness-of-fit statistics derived from the process n1/2(An−Aθn) depends on the unknown distribution P. It is shown here that if the sequences An and θn of estimators are regular in some sense, a parametric bootstrap approach yields valid approximations...

Variables finitas condicionalmente especificadas.

Román Pérez Villalta (2000)

Qüestiió

En este trabajo se estudia la existencia y unicidad de vectores bidimensionales de variables discretas con recorrido finito, cuando se fijan sus distribuciones condicionadas. Para ello, tras repasar la literatura existente sobre el tema, proporcionamos diversos resultados que relacionan diversos temas de álgebra matricial, especialmente la descomposición singular, con el problema que nos ocupa.

Variance components and an additional experiment

Lubomír Kubáček (2012)

Applications of Mathematics

Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.

Variance components and nonlinearity

Lubomír Kubáček, Eva Tesaříková (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the...

Variance function estimation via model selection

Teresa Ledwina, Jan Mielniczuk (2010)

Applicationes Mathematicae

The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted...

Variance of Plug-in Estimators in Multivariate Regression Models

Lubomír Kubáček, Jana Vrbková (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Variance components in regression models are usually unknown. They must be estimated and it leads to a construction of plug–in estimators of the parameters of the mean value of the observation matrix. Uncertainty of the estimators of the variance components enlarge the variances of the plug–in estimators. The aim of the paper is to find this enlargement.

Variations on undirected graphical models and their relationships

David Heckerman, Christopher Meek, Thomas Richardson (2014)

Kybernetika

We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that...

Vingt analyses multivariées d'une structure connue

H. Le Bras (1974)

Mathématiques et Sciences Humaines

L'usage croissant des analyses multivariées modifie la méthode de plusieurs sciences sociales. Le débat sur leur validité est toutefois assez confus car des questions de pure mathématique se mélangent à des problèmes perceptifs (représentation) et logiques (modélisation). Nous n'avons actuellement ni les moyens ni l'ambition d'aborder théoriquement leur statut, mais nous pensons fournir un document utile au débat en appliquant la majorité des méthodes à un même objet déjà connu et en comparant leur...

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