arXiv subjects

E. Lebarbier

Publications and source records attributed to E. Lebarbier.

4 recordsLinked to original sources

arXiv2023

Multiple change-point detection for Poisson point processes

The aim of change-point detection is to identify behavioral shifts within time series data. This article focuses on scenarios where the data is derived from an inhomogeneous Poisson process or a marked Poisson process. We present a methodology for detecting multiple offline change-points using a minimum contrast estimator. Specifically, we address how to manage the continuous nature of the process given the available discrete observations. Additionally, we select the appropriate number of changes via a cross-validation procedure which is particularly effective given the characteristics of the Poisson process. Lastly, we show how to use this methodology for self-exciting processes with changes in the intensity. Through experiments, with both simulated and real datasets, we showcase the advantages of the proposed method, which has been implemented in the R package.

stat.ME↗

arXiv2019

A novel regularized approach for functional data clustering: An application to milking kinetics in dairy goats

Motivated by an application to the clustering of milking kinetics of dairy goats, we propose in this paper a novel approach for functional data clustering. This issue is of growing interest in precision livestock farming that has been largely based on the development of data acquisition automation and on the development of interpretative tools to capitalize on high-throughput raw data and to generate benchmarks for phenotypic traits. The method that we propose in this paper falls in this context. Our methodology relies on a piecewise linear estimation of curves based on a novel regularized change-point estimation method and on the k-means algorithm applied to a vector of coefficients summarizing the curves. The statistical performance of our method is assessed through numerical experiments and is thoroughly compared with existing ones. Our technique is finally applied to milk emission kinetics data with the aim of a better characterization of inter-animal variability and toward a better understanding of the lactation process.

stat.AP↗

arXiv2016

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 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 proposed by Lévy-Leduc et al. [2014] 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 onedimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.

math.ST↗

arXiv2009

Estimating the joint distribution of independent categorical variables via model selection

Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial sequence. A new estimator for this mean is proposed that is nonparametric, non-asymptotic and implementable even for large sequences. It is a penalized least-squares estimator based on wavelets, with a penalization term inspired by papers of Birgé and Massart. The estimator is proved to satisfy an oracle inequality and to be adaptive in the minimax sense over a class of Besov bodies. The method is embedded in a general framework which allows us to recover also an existing method for segmentation. Beyond theoretical results, a simulation study is reported and an application on real data is provided.

math.ST↗