ASYMPTOTIC THEORY FOR SOME HIGH BREAKDOWN POINT ESTIMATORS

High Breakdown Multivariate Estimators

In the literature, estimators for regression or multivariate location and dispersion that have been shown to be both consistent and high breakdown are impractical to compute. This paper gives easily computed high breakdown robust √ n consistent estimators, and the applications for these estimators are numerous. For regression, the response plot of the fitted values versus the response is shown ...

Asymptotic theory for M-estimators of boundaries

A Subsampling Method for the Computation of Multivariate Estimators with High Breakdown Point

· _ All known robust location and scale estimators with high breakdown point for multivariate sample's are very expensive to compute. In practice, this computation has to be carried out using an approximate subsampling procedure. In this work we describe an alternative subsampling scheme, applicable to both the Stahel-Donoho estimator and the estimator based on the Minimum Volume Ellipsoid, wit...

Multivariate Outlier Detection With High-Breakdown Estimators

Multivariate Outlier Detection With High-Breakdown Estimators Andrea Cerioli Andrea Cerioli is Professor, Dipartimento di Economia, Sezione di Statistica e Informatica, Università di Parma, Via Kennedy 6, 43100 Parma, Italy . The author expresses his gratitude to three anonymous reviewers for insightful comments that led to many improvements in the article. The author also thanks Marco Riani an...

Breakdown point theory for implied probability bootstrap

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when an outlier takes an arbitrarily large value, and derive the breakdown points for those bootstrap quantiles. The breakdown properties characterize the situation where the implie...