Adaptive estimation of a density function using beta kernels

Karine Bertin; Nicolas Klutchnikoff

Displaying similar documents to “Adaptive estimation of a density function using beta kernels”

Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation

Van Hanh Nguyen, Catherine Matias (2014)

ESAIM: Probability and Statistics

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In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of -values under the null hypothesis and the other component is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component in the mixture, relying on a preliminary estimator...

Uniform strong consistency of a frontier estimator using kernel regression on high order moments

Stéphane Girard, Armelle Guillou, Gilles Stupfler (2014)

ESAIM: Probability and Statistics

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We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.

Minimax and bayes estimation in deconvolution problem

Mikhail Ermakov (2008)

ESAIM: Probability and Statistics

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We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function where and is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza (2012)

ESAIM: Probability and Statistics

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In this paper, we are interested in estimation problem for the drift parameters matrices of independent multivariate diffusion processes. More specifically, we consider the case where the -parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance...

Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza (2012)

ESAIM: Probability and Statistics

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Two-point priors and minimax estimation of a bounded parameter under convex loss

Agata Boratyńska (2005)

Applicationes Mathematicae

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The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.

Asymptotic unbiased density estimators

Nicolas W. Hengartner, Éric Matzner-Løber (2009)

ESAIM: Probability and Statistics

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This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as , where we see an improvement of as much as 20% over the traditionnal estimator. ...

On-line nonparametric estimation.

Rafail Khasminskii (2004)

SORT

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A survey of some recent results on nonparametric on-line estimation is presented. The first result deals with an on-line estimation for a smooth signal S(t) in the classic 'signal plus Gaussian white noise' model. Then an analogous on-line estimator for the regression estimation problem with equidistant design is described and justified. Finally some preliminary results related to the on-line estimation for the diffusion observed process are described.

Posterior regret Γ-minimax estimation in a normal model with asymmetric loss function

Agata Boratyńska (2002)

Applicationes Mathematicae

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The problem of posterior regret Γ-minimax estimation under LINEX loss function is considered. A general form of posterior regret Γ-minimax estimators is presented and it is applied to a normal model with two classes of priors. A situation when the posterior regret Γ-minimax estimator, the most stable estimator and the conditional Γ-minimax estimator coincide is presented.

Unbiased risk estimation method for covariance estimation

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

ESAIM: Probability and Statistics

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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.

Density smoothness estimation problem using a wavelet approach

Karol Dziedziul, Bogdan Ćmiel (2014)

ESAIM: Probability and Statistics

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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...

Adaptive density estimation for clustering with gaussian mixtures

C. Maugis-Rabusseau, B. Michel (2013)

ESAIM: Probability and Statistics

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Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum likelihood estimator is proposed for automatically selecting the number of mixture components. In the present paper, a collection of univariate densities whose logarithm is locally -Hölder with moment and tail conditions are considered. We show that this...