Showing papers by "Jean-Michel Loubes published in 2013"

Statistical properties of the quantile normalization method for density curve alignment.

Abstract: The article investigates the large sample properties of the quantile normalization method by Bolstad et al. (2003) [4] which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as a particular case of the structural expectation procedure for curve alignment, which corresponds to a notion of barycenter of measures in the Wasserstein space. Moreover, we show that, this method fails in some case of mixtures, and we propose a new methodology to cope with this issue.

LAN property for some fractional type Brownian motion

Abstract: We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density $f_\theta$. We consider the case where $f_\theta\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(\theta)}L_\theta(x)$ with $L_\theta$ a slowly varying function and $\al\PAR{\theta}\in (-\infty,1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B^\alpha_t,\: \alpha \geq 1/2$ or ARFIMA processes.

Method for estimating a journey time of a vehicle on a road network

Abstract: The invention relates to a method for estimating, by a computer, a journey time of a vehicle on a road network, the road network being defined in the form of a mesh comprising a plurality of segments x, each segment x being associated with a mean speed unaffected by weather conditions (Va) for crossing the segment, each segment x being associated with a worsened state (M) of weather conditions, the method including: a step of calculating a mean speed affected by weather conditions (Vc) for crossing the segment from the mean speed unaffected by weather conditions (Va) and climate-modelling parameters (P, P*) defined locally for each segment x in accordance with the worsened state (M) of weather conditions; a step of calculating the time required to cross a segment x at a crossing time t from the mean speed affected by weather conditions (Vc) for the given segment x; and a step of calculating the journey time from the calculation of the time required to cross the segments x.

Rates of convergence in conditional covariance matrix estimation

Abstract: Let $X\in \mathbb{R} ^p$ and $Y\in \mathbb{R}$ two random variables. In this paper we are interested in the estimation of the conditional covariance matrix $Cov(E[\boldsymbol{X}\vert Y])$. To this end, we will use a plug-in kernel based algorithm. Then, we investigate the related performance under smoothness assumptions on the density function of $(\boldsymbol{X},Y)$. Moreover, in high-dimensional context, we shall improve our estimator to avoid inconsistency issues. In the matrix case, the convergence depends on some structural conditions over the $Cov(E[\boldsymbol{X}\vert Y])$.

Statistical properties of the quantile normalization method for density curve alignment

Abstract: The article investigates the large sample properties of the quantile normalization method by Bolstad et al. (2003) [4] which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as a particular case of the structural expectation procedure for curve alignment, which corresponds to a notion of barycenter of measures in the Wasserstein space. Moreover, we show that, this method fails in some case of mixtures, and we propose a new methodology to cope with this issue.

Rates of convergence in conditional covariance matrix with nonparametric entries estimation

Abstract: Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables We estimate the conditional covariance matrix $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ applying a plug-in kernel-based algorithm to its entries Next, we investigate the estimators rate of convergence under smoothness hypotheses on the density function of $(\boldsymbol{X},Y)$ In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ entries We illustrate a sliced inverse regression setting for time series matching the conditions of our estimator

Kernel Inverse Regression for random fields

Abstract: In this paper, we propose a Dimension Reduction model for spatially dependent variables. Namely, we investigate a generalization of the Inverse Regression method under some mixing conditions. This method introduced by (Li, 1991) for i.i.d. data is based on the estimation of the matrix of covariance of the conditional expectation of the explanatory variable given the response variable. Here, we investigate the weak consistency of this estimate based on a kernel estimate of the Inverse Regression under strong mixing condition. Through some simulations, we show the difference of behavior between our method and its i.i.d. counterpart. We also, investigate applications of our method in spatial forecasting problems and confront its with some others whom make their proof through a real data application.

Functional calibration estimation by the maximum entropy on the mean principle

Abstract: We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling but considering a functional data framework. The functional calibration sampling weights of the estimator are obtained by matching the calibration estimation problem with the maximum entropy on the mean principle. In particular, the calibration estimation is viewed as an infinite dimensional linear inverse problem following the structure of the maximum entropy on the mean approach. We give a precise theoretical setting and estimate the functional calibration weights assuming, as prior measures, the centered Gaussian and compound Poisson random measures. Additionally, through a simple simulation study, we show that our functional calibration estimator improves its accuracy compared with the Horvitz-Thompson estimator.

A Robbins-Monro procedure for the estimation of parametric deformations on random variables

Abstract: The paper is devoted to the study of a parametric deformation model of independent and identically random variables. Firstly, we construct an efficient and very easy to compute recursive estimate of the parameter. Our stochastic estimator is similar to the Robbins-Monro procedure where the contrast function is the Wasserstein distance. Secondly, we propose a recursive estimator similar to that of Parzen-Rosenblatt kernel density estimator in order to estimate the density of the random variables. This estimate takes into account the previous estimation of the parameter of the model. Finally, we illustrate the performance of our estimation procedure on simulations for the Box-Cox transformation and the arcsinh transformation.