Séance Séminaire

Séminaire de Probabilités et Statistique

Semiparametric models for time-dependent data using Lasso-type estimators

In many applications, multiple measurements are made on one or several experimental units over a period of time. Such data could be called, in a general form, as time-dependent data. From a statistical point of view, if we consider only one experimental unit, we can use a time series or signals analysis. On the other hand, if we consider experimental designs (or observational studies) for several experimental units (or subjects) where each subject is measured at several points in time, we can use the term of repeated measures or more specifically, longitudinal data. The main aim of this talk is to propose novel estimation procedures in two specific kind of time-dependent semiparametric models using a Lasso type estimator. In a first time, we propose new estimation strategies for longitudinal data using a semiparametric nonlinear mixed-effects via a stochastic approximation version of EM algorithm and a Lasso-type method. As a second illustration, we consider a semiparametric approach to perform the joint segmentation of multiple series sharing a common functional part. We propose an iterative procedure base don Dynamic Programming for the segmentation part and Lasso estimators for the functional part. In both cases, our Lasso procedure, based on the dictionary approach, allows us to both estimate smooth functions and functions with local irregularity.