Baba Thiam

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Marie Husková

Charles University, Prague

BORDEAUX INP

University of Siena / Università di Siena

Mohamed Chaouch

University of Reading

Larry Wasserman

Jiti Gao

Piet Groeneboom

Delft University of Technology

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Papers by Baba Thiam

Joint Behaviour of Semirecursive Kernel Estimators of the Location and of the Size of the Mode of a Probability Density Function

Journal of Probability and Statistics, 2011

ABSTRACT Let $\theta$ and $\mu$ denote the location and the size of the mode of a probability den... more ABSTRACT Let $\theta$ and $\mu$ denote the location and the size of the mode of a probability density. We study the joint convergence rates of semirecursive kernel estimators of $\theta$ and $\mu$. We show how the estimation of the size of the mode allows to measure the relevance of the estimation of its location. We also enlighten that, beyond their computational advantage on nonrecursive estimators, the semirecursive estimators are preferable to use for the construction on confidence regions.

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Segmentation simultanée de signaux: application aux données de microarray CGH

Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives

In this paper we prove large and moderate deviations principles for the recursive kernel estimato... more In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behavior not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the uniform deviations.

Joint segmentation, calling, and normalization of multiple CGH profiles

by Baba Thiam and Stéphane Robin

Biostatistics

The statistical analysis of array comparative genomic hybridization (CGH) data has now shifted to... more The statistical analysis of array comparative genomic hybridization (CGH) data has now shifted to the joint assessment of copy number variations at the cohort level. Considering multiple profiles gives the opportunity to correct for systematic biases observed on single profiles, such as probe GC content or the so-called "wave effect." In this article, we extend the segmentation model developed in the univariate case to the joint analysis of multiple CGH profiles. Our contribution is multiple: we propose an integrated model to perform joint segmentation, normalization, and calling for multiple array CGH profiles. This model shows great flexibility, especially in the modeling of the wave effect that gives a likelihood framework to approaches proposed by others. We propose a new dynamic programming algorithm for break point positioning, as well as a model selection criterion based on a modified bayesian information criterion proposed in the univariate case. The performance of...

Statistical assessment of chromosomal aberrations at the cohort level: the CGHSeg package

ABSTRACT Segmentation methods have been successfully applied to the mapping of chromosomal abnorm... more ABSTRACT Segmentation methods have been successfully applied to the mapping of chromosomal abnormalities when using CGH microarrays. Most current methods deal with one CGH profile only, and do not integrate multiple arrays, whereas the CGH microarray technology becomes widely used to characterize chromosomal defaults at the cohort level. We present CGHSeg, an R package that is devoted to the analysis of CGH profiles at the individual and at the cohort levels. This package performs segmentation in multiple CGH profiles in the framework of linear models, and multivariate segmentation/clustering for the joint characterization of aberration types (status assignment of regions based on the cohort). Overall, linear models offer a unified framework for the joint analysis of multiple CGH profiles, and we will show how they can be used to link the experience acquired in the field of expression arrays (normalization, experimental design) with array CGH data analysis.

Optimal rank-based inference for spherical location

by Christophe Ley and Baba Thiam

A smoothing stochastic algorithm for quantile estimation

Statistics & Probability Letters, 2014

ABSTRACT In this paper, we provide the almost-sure convergence and the asymptotic normality of a ... more

R-estimation d’un parametre de position sur la sphere unité

by Christophe Ley and Baba Thiam

... 50, Avenue Roosevelt CP 114, 1050, Bruxelles, Belgique [email protected] [email protected]. be 2 ... more

Robust quantile estimation and prediction for spatial processes

Statistics & Probability Letters, 2010

In this paper, we present a statistical framework for modeling conditional quantiles of spatial p... more In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the L1 consistency and the asymptotic normality of the kernel conditional quantile estimator in the case of random fields. We also define a nonparametric spatial predictor and illustrate the methodology used with some simulations.

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Large and moderate deviations principles for kernel estimators of the multivariate regression

Mathematical Methods of Statistics, 2008

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the ... more In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the unidimensional case for the Nadaraya-Watson estimator. Moreover, we give a moderate deviations principle for these two estimators. It turns out that the rate function obtained in the moderate deviations principle for the semi-recursive estimator is larger than the one obtained for the Nadaraya-Watson estimator.

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Consistency of the recursive nonparametric regression estimation for dependent functional data

Journal of Nonparametric Statistics, 2014

ABSTRACT We consider the recursive estimation of a regression functional where the explanatory va... more ABSTRACT We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition.

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Recursive estimation of nonparametric regression with functional covariate

Computational Statistics & Data Analysis, 2014

The main purpose is to estimate the regression function of a real random variable with functional... more The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real data set studies.

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