Asymptotic theory of outlier detection algorithms for linear time series regression models

Journal article

Outlier detection algorithms are intimately connected with robust statistics that down-weight some observations to zero. We deÖne a number of outlier detection algorithms related to the Huber-skip and the Least Trimmed Squares estimators, including the 1-step Huber skip estimator and the Forward Search. Next, we review a recently developed asymptotic theory of these. Finally, we analyze the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.

Authors: Johansen, S; Nielsen, B

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Wiley
• Journal: Scandinavian Journal of Statistics
• Acceptance date: 2015-06-26
• EISSN: 1467-9469
• ISSN: 0303-6898
• Language: English
• Keywords: Huber-skip; iteration of 1-step estimators; weighted and marked empirical processes; robustified least squares; 1-step Huber-skip; Impulse Indicator Saturation; Forward Search; iterated martingale inequality; gauge