Composite Robust Estimators for Linear Mixed Models

CLAUDIO AGOSTINELLI; VÍCTOR J. YOHAI

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

AMER STATISTICAL ASSOC

Lugar: Washington; Año: 2016 vol. 111 p. 1764 - 1774

0162-1459

The Classical Tukey-Huber Contamination Model (CCM) is a commonly adopted framework to describe the mechanism of outliers generation in robust statistics. Given a data set with n observations and p variables, under the CCM, an outlier is a unit, even if only one or a few values are corrupted. Classical robust procedures were designed to cope with this type of outliers. Recently, a new mechanism of outlier generation was introduced, namely the Independent Contamination Model (ICM), where the occurrences that each cell of the data matrix is an outlier are independent events and have the same probability. ICM poses new challenges to robust statistics since the percentage of contaminated rows dramatically increase with p, often reaching more than 50% whereas classical affine equivariant robust procedures have a breakdown point of 50% at most. For ICM we propose a new type of robust methods namely composite robust procedures which are inspired by the idea of composite likelihood, where low dimension likelihood, very often the likelihood of pairs, are aggregated in order to obtain a tractable approximation of the full likelihood. Our composite robust procedures are build on pairs of observations in order to gain robustness in the ICM. We propose composite tau-estimators for linear mixed models. Composite tau-estimators are proved to have a high breakdown point both in the CCM and ICM. A Monte Carlo study shows that while classical S-estimators can only cope with outliers generated by the CCM, the estimators proposed here are resistant to both CCM and ICM outliers.