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 our method is assessed using simulated and real data sets. Our method is implemented in the R package cghseg.

In this paper, we provide R-estimators of the location of a rotationally symmetric distribution on the unit sphere of R-k. In order to do so we first prove the local asymptotic normality property of a sequence of rotationally symmetric models; this is a non-standard result due to the curved nature of the unit sphere. We then construct our estimators by adapting the Le Cam one-step methodology to spherical statistics and ranks. We show that they are asymptotically normal under any rotationally symmetric distribution and achieve the efficiency bound under a specific density. Their small sample behavior is studied via a Monte Carlo simulation and our methodology is illustrated on geological data

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.