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Displaying 281 – 298 of 298

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...

Variable selection through CART

Marie Sauve, Christine Tuleau-Malot (2014)

ESAIM: Probability and Statistics

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...

Variational theorems in gnostical theory of uncertain data

Jan Šindelář (1995)

Kybernetika

Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation

Gérard Collomb, Pascal Sarda, Philippe Vieu (1985)

Commentationes Mathematicae Universitatis Carolinae

Weighted halfspace depth

Daniel Hlubinka, Lukáš Kotík, Ondřej Vencálek (2010)

Kybernetika

Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.

Why minimax is not that pessimistic

Aurelia Fraysse (2013)

ESAIM: Probability and Statistics

In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense...

Zur Schätzung eines Dichtefunktionals.

L. Schüler, H. Wolff (1976)

Metrika

ε-Entropy and moduli of smoothness in $L^{p}$ -spaces

A. Kamont (1992)

Studia Mathematica

The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in $L^{p} (^{d})$ is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in $L^{p} (ℝ^{d})$ whose tail function decreases as $O (λ^{- γ})$ is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on $ℝ^{d}$ and the minimax risk for that class is discussed.