Robust semi-parametric multiple change-points detection

Abstract

This paper is dedicated to define two new multiple change-points detectors in the case of an unknown number of changes in the mean of a signal corrupted by additive noise. Both these methods are based on the Least-Absolute Value (LAV) criterion. Such criterion is well known for improving the robustness of the procedure, especially in the case of outliers or heavy-tailed distributions. The first method is inspired by model selection theory and leads to a data-driven estimator. The second one is an algorithm based on total variation type penalty. These strategies are numerically studied on Monte-Carlo experiments.

Change-point detection, segmentation, and related topics

“…The heuristic slope procedure has been introduced in [1]. It was applied in the three previous framework (see respectively [4] or [35], [6] and [5]) for deducing a data-driven penalization. In the sequel we detail the case of long-memory change detection.…”

“…be an estimator of the number of changes using the data-driven procedure. we have shown that this data-driven procedure leads to more accurate results than the procedures based on penalization with a sequence (κ n ) chosen a priori (see in [4] and [35] for the result for Framework 1, [6] for Framework 2, and [5] for the case of Framework 3). In the research about the autonomous vehicles, the cost of a high performance GPS is a problem and a solution proposed is to study the environment of the vehicles to guide the latter in the case of regular trips.…”

Laplace’s method and BIC model selection for least absolute value criterion

“…Its two main advantages are, first, that it does not require strong moment conditions to converge or to be asymptotically Gaussian, and second, that it is significantly more robust (see for instance [9]), especially to the presence of possible outliers. It has for example been studied in the context of the detection of breaks in [4] and [2] (for shifts) and [5] (for linear models), for the estimation of parameters of time series, as in [7] (for ARMA processes) or in [1] (for affine causal processes). It also opens the way to more complex procedures, such as robust regression with Huber function (see [8]) or quantile regression (see [11]).…”