Estimating the number of block boundaries from diagonal blockwise matrices without penalization
2017
Brault, Vincent | Delattre, Maud | Mary-Huard, Tristan | Leduc, Céline | Mathématiques et Informatique Appliquées (MIA-Paris) ; Institut National de la Recherche Agronomique (INRA)-AgroParisTech | Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale) (GQE-Le Moulon) ; Institut National de la Recherche Agronomique (INRA)-Université Paris-Sud - Paris 11 (UP11)-AgroParisTech-Centre National de la Recherche Scientifique (CNRS) | French National Research Agency ANR through the ABS4NGS project ANR-11-BINF-0001-06 | ANR-11-BINF-0001,ABS4NGS,Solutions Algorithmiques, Bioinformatiques et Logicielles pour le Séquençage Haut Débit(2011)
In computational biology, numerous recent studies have been dedicated to the analysis of the chromatin structure within the cell by two-dimensional segmentation methods. Motivated by this application, we consider the problem of retrieving the diagonal blocks in a matrix of observations. The theoretical properties of the least squares estimators of both the boundaries and the number of blocks are investigated. More precisely, the contribution of the paper is to establish the consistency of these estimators. A surprising consequence of our results is that, contrary to the one-dimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.
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