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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...

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...

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