Céline Lévy-Leduc

Multiple Change-Point Estimation With a Total Variation Penalty

We propose a new approach for dealing with the estimation of the location of change-points in one-dimensional piecewise constant signals observed in white noise. Our approach consists in reframing this task in a variable selection context. We use a penalized least-square criterion with a ℓ1-type penalty for this purpose. We explain how to implement this method in practice by using the LARS / LASSO algorithm. We then prove that, in an appropriate asymptotic framework, this method provides consistent estimators of the change points with an almost optimal rate. We finally provide an improved practical version of this method by combining it with a reduced version of the dynamic programming algorithm and we successfully compare it with classical methods.

Robust Estimation of the Scale and of the Autocovariance Function of Gaussian Short- and Long-Range Dependent Processes

A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an autocovariance estimator which is robust to additive outliers can be very useful for time-series modeling. In this paper, the asymptotic properties of the robust scale and autocovariance estimators proposed by Rousseeuw and Croux (1993) and Genton and Ma (2000) are established for Gaussian processes, with either short-range or long-range dependence. It is shown in the short-range dependence setting that this robust estimator is asymptotically normal at the rate

Asymptotic properties of U-processes under long-range dependence

\sqrt{n}

Robust changepoint detection based on multivariate rank statistics

, where

Distributed detection/localization of change-points in high-dimensional network traffic data

n

Robust retrospective multiple change-point estimation for multivariate data

is the number of observations. An explicit expression of the asymptotic variance is also given and compared to the asymptotic variance of the classical autocovariance estimator. In the long-range dependence setting, the limiting distribution displays the same behavior than that of the classical autocovariance estimator, with a Gaussian limit and rate

Sequential Design of Computer Experiments for the Assessment of Fetus Exposure to Electromagnetic Fields

\sqrt{n}

Frequency estimation based on the cumulated Lomb-Scargle periodogram

when the Hurst parameter

A variable selection approach in the multivariate linear model: an application to LC-MS metabolomics data

H

Efficient block boundaries estimation in block-wise constant matrices: An application to HiC data

is less