Page 1 Next

Displaying 1 – 20 of 159

Showing per page

A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

Michael H. Neumann (2013)

ESAIM: Probability and Statistics

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics...

A class of unbiased kernel estimates of a probability density function

Tomasz Rychlik (1995)

Applicationes Mathematicae

We propose a class of unbiased and strongly consistent nonparametric kernel estimates of a probability density function, based on a random choice of the sample size and the kernel function. The expected sample size can be arbitrarily small and mild conditions on the local behavior of the density function are imposed.

A comparison of automatic histogram constructions

Laurie Davies, Ursula Gather, Dan Nordman, Henrike Weinert (2009)

ESAIM: Probability and Statistics

Even for a well-trained statistician the construction of a histogram for a given real-valued data set is a difficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the bins in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction procedures by means of a simulation study. The study includes plug-in methods, cross-validation, penalized maximum likelihood and the taut string...

A non asymptotic penalized criterion for gaussian mixture model selection

Cathy Maugis, Bertrand Michel (2011)

ESAIM: Probability and Statistics

Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...

A non asymptotic penalized criterion for Gaussian mixture model selection

Cathy Maugis, Bertrand Michel (2012)

ESAIM: Probability and Statistics

Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...

A note on robust estimation in logistic regression model

Tadeusz Bednarski (2016)

Discussiones Mathematicae Probability and Statistics

Computationally attractive Fisher consistent robust estimation methods based on adaptive explanatory variables trimming are proposed for the logistic regression model. Results of a Monte Carlo experiment and a real data analysis show its good behavior for moderate sample sizes. The method is applicable when some distributional information about explanatory variables is available.

A note on the adaptive estimation of the differential entropy by wavelet methods

Christophe Chesneau, Fabien Navarro, Oana Silvia Serea (2017)

Commentationes Mathematicae Universitatis Carolinae

In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean 𝕃 p error, p 1 , this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.

A probability density function estimation using F-transform

Michal Holčapek, Tomaš Tichý (2010)

Kybernetika

The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method...

Adaptive Dantzig density estimation

K. Bertin, E. Le Pennec, V. Rivoirard (2011)

Annales de l'I.H.P. Probabilités et statistiques

The aim of this paper is to build an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose a minimization of the ℓ1-norm of the coefficients in the linear combination under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global structure assumptions, oracle inequalities are derived. These theoretical results are transposed...

Adaptive density estimation for clustering with gaussian mixtures

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

ESAIM: Probability and Statistics

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 β-Hölder with moment and tail conditions are considered. We show that this penalized...

Adaptive density estimation under weak dependence

Irène Gannaz, Olivier Wintenberger (2010)

ESAIM: Probability and Statistics

Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue's measure. [Donoho et al. Ann. Stat.24 (1996) 508–539] propose near-minimax estimators f ^ n based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are...

Adaptive estimation of a density function using beta kernels

Karine Bertin, Nicolas Klutchnikoff (2014)

ESAIM: Probability and Statistics

In this paper we are interested in the estimation of a density − defined on a compact interval of ℝ− from n independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski’s method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator using simulated...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2010)

ESAIM: Probability and Statistics

We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U-statistics of order 2 due to Houdré and Reynaud.

Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte, Florence Merlevède (2002)

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of the stationary marginal density f of an α or a β -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate f using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed via the minimization...

Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte, Florence Merlevède (2010)

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of the stationary marginal density f of an α or a β-mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate f using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed via the minimization...

Currently displaying 1 – 20 of 159

Page 1 Next