Segmentation of the Poisson and negative binomial rate models: a penalized estimator

We consider the segmentation problem of Poisson and negative binomial (i.e. overdispersed Poisson) rate distributions. In segmentation, an important issue remains the choice of the number of segments. To this end, we propose a penalized log-likelihood estimator where the penalty function is constructed in a non-asymptotic context following the works of L. Birg\'e and P. Massart. The resulting estimator is proved to satisfy an oracle inequality. The performances of our criterion is assessed using simulated and real datasets in the RNA-seq data analysis context

Detecting Multiple Change-Points in the Mean of Gaussian Process by Model Selection

This paper deals with the problem of detecting the change-points in mean of a signal corrupted by an additive Gaussian noise. The number of changes and their positions are unknown. From a nonasymptotic point of view, we propose to estimate them with a method based on a penalized least-squares criterion. According to the results of Birgé and Massart, we choose the penalty function such that the resulting estimator minimizes the quadratic risk. This penalty depends on unknown constants and we propose a calibration leading to an automatic method. The performances of the method are assessed through simulation experiments. An application to real data is shown

Classification of longitudinal data through a semiparametric mixed-effects model based on lasso-type estimators

We propose a classification method for longitudinal data. The Bayes classifier is classically used to determine a classification rule where the underlying density in each class needs to be well modeled and estimated. This work is motivated by a real dataset of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. The proposed model, which is a semiparametric linear mixed-effects model (SLMM), is a particular case of the semiparametric nonlinear mixed-effects class of models (SNMM) in which finite dimensional (fixed effects and variance components) and infinite dimensional (an unknown function) parameters have to be estimated. In SNMM’s maximum likelihood estimation is performed iteratively alternating parametric and nonparametric procedures. However, if one can make the assumption that the random effects and the unknown function interact in a linear way, more efficient estimation methods can be used. Our contribution is the proposal of a unified estimation procedure based on a penalized EM-type algorithm. The Expectation and Maximization steps are explicit. In this latter step, the unknown function is estimated in a nonparametric fashion using a lasso-type procedure. A simulation study and an application on real data are performed.The authors are grateful to two anonymous referees and an Associate Editor for their insightful comments and valuable suggestions, which led to substantial improvements in the presentation of this work. Ana Arribas–Gil was supported by projects MTM2010-17323 and ECO2011-25706, Spain. Rolando de la Cruz was supported by project FONDECYT 1120739, grant ANILLO ACT–87, and grant FONDAP 15130011, Chile. Cristian Meza was supported by projects FONDECYT 11090024 and 1141256, and grant ANILLO ACT–1112, CONICYT-PIA, Chile