Valeurs extrémales de suites stationnaires de variables aléatoires m-dépendantes
Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models
In testing that a given distribution Pbelongs to a parameterized family , 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...
Variable selection through CART
This paper deals with variable selection in regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This work, of theoretical nature, aims at determining adequate penalties, i.e. penalties which allow achievement of oracle type inequalities justifying the performance of the proposed procedure. Since the exhaustive procedure cannot be realized when the number of variables...
Variance function estimation via model selection
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...
Variational theorems in gnostical theory of uncertain data
Various limit theorems for ratios from the uniform distribution
In this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.
Verbesserung des nicht-randomisierten exakten Testes von R.A. Fisher
Vergleich des verallgemeinerten nichtzentralen t-Tests mit dem Binomialtest.
Verhalten des Chi-Quadrat-Tests für Prüfung der Gleichwahrscheinlichkeit der Lotto-Zahlen bei Nichtgültigkeit der Hypothese.