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. 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.
Mots clés : distribution estimation, change-point detection, count data (RNA-seq), poisson and negative binomial distributions, model selection
@article{PS_2014__18__750_0,
author = {Cleynen, Alice and Lebarbier, Emilie},
title = {Segmentation of the {Poisson} and negative binomial rate models: a penalized estimator},
journal = {ESAIM: Probability and Statistics},
pages = {750--769},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2014005},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2014005/}
}
TY - JOUR AU - Cleynen, Alice AU - Lebarbier, Emilie TI - Segmentation of the Poisson and negative binomial rate models: a penalized estimator JO - ESAIM: Probability and Statistics PY - 2014 SP - 750 EP - 769 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2014005/ DO - 10.1051/ps/2014005 LA - en ID - PS_2014__18__750_0 ER -
%0 Journal Article %A Cleynen, Alice %A Lebarbier, Emilie %T Segmentation of the Poisson and negative binomial rate models: a penalized estimator %J ESAIM: Probability and Statistics %D 2014 %P 750-769 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2014005/ %R 10.1051/ps/2014005 %G en %F PS_2014__18__750_0
Cleynen, Alice; Lebarbier, Emilie. Segmentation of the Poisson and negative binomial rate models: a penalized estimator. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 750-769. doi : 10.1051/ps/2014005. http://archive.numdam.org/articles/10.1051/ps/2014005/
[1] , Information Theory and Extension of the Maximum Likelihood Principle. Second int. Symp. Inf. Theory (1973) 267-281. | MR | Zbl
[2] , Estimating a discrete distribution via histogram selection. ESAIM: PS 15 (2011) 1-29. | EuDML | MR
[3] and , Data-driven calibration of penalties for least-squares regression. J. Mach. Learn. Res. 10 (2009) 245-279.
[4] and , Estimating the intensity of a random measure by histogram type estimators. Probab. Theory Relat. Fields (2009) 143 239-284. | MR | Zbl
[5] , and , Risk bounds for model selection via penalization. Probab. Theory Relat. Fields 113 (1999) 301-413. | MR | Zbl
[6] , , , Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence 22 (2000) 719-725.
[7] , Model selection for Poisson processes. In Asymptotics: particles, processes and inverse problems, Vol. 55 of IMS Lect. Notes Monogr. Ser.. Beachwood, OH: Inst. Math. Statist. (2007) 32-64. | MR | Zbl
[8] and , From model selection to adaptive estimation, in Festschrift for Lucien Le Cam. New York, Springer (1997) 55-87. | MR | Zbl
[9] and , Gaussian model selection. J. Eur. Math. Soc. 3 (2001) 203-268. | EuDML | MR | Zbl
[10] and , Minimal penalties for Gaussian model selection. Probab. Theory Relat. Fields (2007) 138 33-73. | MR | Zbl
[11] , and , Multiple changepoint fitting via quasilikelihood, with application to DNA sequence segmentation. Biometrika 87 (2000) 301-314. | MR | Zbl
[12] , , Statistical methods for DNA sequence segmentation. Stat. Sci. (1998) 142-162. | Zbl
[13] , : Classification and Regression Trees. Wadsworth and Brooks (1984). | Zbl
[14] , Modified Akaikes criterion for histogram density estimation. Technical Report#9961 (1999).
[15] , , , and , Segmentor3IsBack, an R package for the fast and exact segmentation of Seq-data. Algorithms for Molecular Biology (2014)
[16] , and , Univariate Discrete Distributions. John Wiley & Sons, Inc. (2005). | MR | Zbl
[17] and , Changepoint: an R package for changepoint analysis. Lancaster University (2011).
[18] , Detecting multiple change-points in the mean of Gaussian process by model selection. Signal Process. 85 (2005) 717-736. | Zbl
[19] , and , Fast estimation of posterior probabilities in change-point analysis through a constrained hidden Markov model. Comput. Stat. Data Anal. (2013). | MR
[20] , Concentration inequalities and model selection. In Lect. Notes Math. Springer Berlin/Heidelberg (2007). | MR | Zbl
[21] , Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities. Probab. Theory Relat. Fields 126 (2003) 103-153. | MR | Zbl
[22] , Pruned dynamic programming for optimal multiple change-point detection. ArXiv:1004.0887 2010, [http://arxiv.org/abs/1004.0887].
[23] , and , Exact posterior distributions and model selection criteria for multiple change-point detection problems. Stat. Comput. 22 (2012) 917-929. | MR | Zbl
[24] , , and , GC-Content Normalization for RNA-Seq Data. BMC Bioinform. 12 (2011) 480.
[25] , Estimating the number of change-points via Schwarz' criterion. Stat. Probab. Lett. 6 (1988) 181-189. | MR | Zbl
[26] and , A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data. Biometrics 63 (2007) 22-32. | MR | Zbl
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