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

This paper deals with the problem of detecting change-points in the mean of count-data modelled by a discrete distribution where the number of change-points is unknown. We consider here two distributions: Poisson and negative binomial (adapted to the RNA-seq experiment analysis). We propose a new penalized log-likelihood estimator for the true distribution in a non-parametric and non-asymptotic density estimation context. The choice of the penalty term of this criterion is inspired of papers of Birg\'e and Massart, i.e. constructed such that the resulting estimator satisfies an oracle inequality. An application concerning RNA-seq data analysis is provided.