Estimating the number of change-points in a two-dimensional segmentation model without penalization

In computational biology, numerous recent studies have been dedicated to the analysis of chromatin structure within the cell via 2-dimension signal segmentation analysis. Motivated by this application, the problem of retrieving the diagonal blocks in a matrix of observations is considered. More precisely, the theoretical properties of the (slightly modified) least-squares estimators of both the boundaries and the number of blocks are investigated. The main novelty of the present paper is that, contrary to the one-dimensional case, penalization is useless for retrieving the true number of diagonal blocks. These results are illustrated on simulated data.