Displaying similar documents to “Oracle inequalities and nonparametric function estimation.”

Density smoothness estimation problem using a wavelet approach

Karol Dziedziul, Bogdan Ćmiel (2014)

ESAIM: Probability and Statistics

Similarity:

In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, ). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes possible for some classes...

On One Estimation Problem

Jelena Bulatović, Alobodanka Janjić (1979)

Publications de l'Institut Mathématique

Similarity:

Unbiased risk estimation method for covariance estimation

Hélène Lescornel, Jean-Michel Loubes, Claudie Chabriac (2014)

ESAIM: Probability and Statistics

Similarity:

We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.

Numerical methods for linear minimax estimation

Norbert Gaffke, Berthold Heiligers (2000)

Discussiones Mathematicae Probability and Statistics

Similarity:

We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.

Why minimax is not that pessimistic

Aurelia Fraysse (2013)

ESAIM: Probability and Statistics

Similarity:

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,...