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Segmentation of the Poisson and negative binomial rate models: a penalized estimator. (English) Zbl 1310.62041

Summary: 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 likelihood estimator where the penalty function is constructed in a non-asymptotic context following the works of L. Birgé and P. Massart [J. Eur. Math. Soc. (JEMS) 3, No. 3, 203–268 (2001; Zbl 1037.62001); Probab. Theory Relat. Fields 138, No. 1–2, 33–73 (2007; Zbl 1112.62082)]. 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.

MSC:

62G05 Nonparametric estimation
62G07 Density estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
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