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Why $L_{1}$ view and what is next?

László Györfi, Adam Krzyżak (2011)

Kybernetika

N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the $L_{1}$ view of density estimation. The Cencov’s work is available in Russian only and it hasn’t been translated, so late Igor Vajda decided to translate the Cencov’s paper and to add some remarks on the occasion of organizing the session “25 Years of the $L_{1}$ Density Estimation” at the Prague Stochastics 2010 Symposium. In this paper we...

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...

Wild bootstrap in RCA(1) model

Zuzana Prášková (2003)

Kybernetika

In the paper, a heteroskedastic autoregressive process of the first order is considered where the autoregressive parameter is random and errors are allowed to be non-identically distributed. Wild bootstrap procedure to approximate the distribution of the least-squares estimator of the mean of the random parameter is proposed as an alternative to the approximation based on asymptotic normality, and consistency of this procedure is established.

Zur quantitativen Theorie der Gleichverteilung.

H. Niederreiter (1973)

Monatshefte für Mathematik

Zur Schätzung eines Dichtefunktionals.

L. Schüler, H. Wolff (1976)

Metrika

Zur Theorie des Rangtests.

H. Witting (1972)

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.

$φ$ PHI-divergences, sufficiency, Bayes sufficiency, and deficiency

Friedrich Liese (2012)

Kybernetika

The paper studies the relations between $φ$ -divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam’s deficiency. A new and considerably simplified approach is given to the spectral representation of $φ$ -divergences already established in Österreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary...