Semi-parametric segmentation of multiple series using a DP-Lasso strategy

We consider a semi-parametric approach to perform the joint segmentation of multiple series sharing a common functional part. We propose an iterative procedure based on Dynamic Programming for the segmentation part and Lasso estimators for the functional part. Our Lasso procedure, based on the dictionary approach, allows us to both estimate smooth functions and functions with local irregularity, which permits more flexibility than previous proposed methods. This yields to a better estimation of the functional part and improvements in the segmentation. The performance of our method is assessed using simulated data and real data from agriculture and geodetic studies. Our estimation procedure results to be a reliable tool to detect changes and to obtain an interpretable estimation of the functional part of the model in terms of known functions.     

A breakpoint detection in the mean model with heterogeneous variance on fixed time intervals

Statistics and Computing - This work is motivated by an application for the homogenization of global navigation satellite system (GNSS)-derived integrated water vapour series. Indeed, these series...     

Estimating the Number of Block Boundaries from Diagonal Blockwise Matrices Without Penalization

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.     

A factor model approach for the joint segmentation with between‐series correlation

We consider the detection of changes in the mean of a set of time series. The breakpoints are allowed to be series specific, and the series are assumed to be correlated. The correlation between the series is supposed to be constant along time but is allowed to take an arbitrary form. We show that such a dependence structure can be encoded in a factor model. Thanks to this representation, the inference of the breakpoints can be achieved via dynamic programming, which remains one the most efficient algorithms. We propose a model selection procedure to determine both the number of breakpoints and the number of factors. This proposed method is implemented in the FASeg R package, which is available on the CRAN. We demonstrate the performances of our procedure through simulation experiments and present an application to geodesic data.