Comparison of kernel density estimators with assumption on number of modes

International audienceA data-driven bandwidth choice for a kernel density estimator called critical bandwidth is investigated. This procedure allows the estimation to have as many modes as assumed for the density to estimate. Both Gaussian and uniform kernels are considered. For the Gaussian kernel, asymptotic results are given. For the uniform kernel, an argument against these properties is mentioned. These theoretical results are illustrated with a simulation study which compare the kernel estimators that rely on critical bandwidth with another one which uses a plug-in method to select its bandwidth. An estimator that consists in estimates of density contour clusters and takes assumptions on number of modes into account is also considered. Finally, the methodology is illustrated using environment monitoring data

Une interface graphique pour analyser des données distantes sous R

Ce travail présente une méthode pour implémenter des algorithmes d'analyse de données lorsque celles-ci sont stockées sur une machine distante et pour créer une interface graphique facilitant l'utilisation de ces algorithmes. Une application à des estimations de densité dans un contexte biologique est fournie.Une interface graphique pour analyser des données distantes sous

A semiparametric approach to estimate reference curves for biophysical properties of the skin

Reference curves which take one covariable into account such as the age, are often required in medicine, but simple systematic and e±cient statistical methods for constructing them are lacking. Classical methods are based on parametric Øtting (polynomial curves). In this talk, we describe a method- ology for the estimation of reference curves for data sets, based on nonpara- metric estimation of conditional quantiles. The derived method should be applicable to all clinical or more generally biological variables that are mea- sured on a continuous quantitative scale. To avoid the curse of dimensionality when the covariate is multidimensional, a semiparametric approach is pro- posed. This procedure combines a dimension-reduction step (based on sliced inverse regression) and kernel estimation of conditional quantiles step. The usefulness of this semiparametric estimation procedure is illustrated on a sim- ulated data set and on a real data set collected in order to establish reference curves for biophysical properties of the skin of healthy French wome

Evaluation de l’importance des variables dans la méthode SIR (Sliced Inverse Regression)

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Comparison of sliced inverse regression approaches for underdetermined cases

Among methods to analyze high-dimensional data, the sliced inverse regression (SIR) is of particular interest for non-linear relations between the dependent variable and some indices of the covariate. When the dimension of the covariate is greater than the number of observations, classical versions of SIR cannot be applied. Various upgrades were then proposed to tackle this issue such as RSIR and SR-SIR, to estimate the parameters of the underlying model and to select variables of interest. In this paper, we introduce two new estimation methods respectively based on the QZ algorithm and on the Moore-Penrose pseudo-inverse. We also describe a new selection procedure of the most relevant components of the covariate that relies on a proximity criterion between submodels and the initial one. These approaches are compared with RSIR and SR-SIR in a simulation study. Finally we applied SIR-QZ and the associated selection procedure to a genetic dataset in order to find eQTL

On Semiparametric Mode Regression Estimation.

It has been found that, for a variety of probability distributions, there is a surprising linear relation between mode, mean and median. In this paper, the relation between mode, mean and median regression functions is assumed to follow a simple parametric model. We propose a semiparametric conditional mode (mode regression) estimation for an unknown (unimodal) conditional distribution function in the context of regression model, so that any m-step-ahead mean and median forecasts can then be substituted into the resultant model to deliver m-step-ahead mode prediction. In the semiparametric model, Least Squared Estimator (LSEs) for the model parameters and the simultaneous estimation of the unknown mean and median regression functions by the local linear kernel method are combined to infer about the parametric and nonparametric components of the proposed model. The asymptotic normality of these estimators is derived, and the asymptotic distribution of the parameter estimates is also given and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model. These results are applied to obtain a data-based test for the dependence of mode regression over mean and median regression under a regression model

Estimation des quantiles géométriques conditionnels et non conditionnels

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