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

摘要

Outlier detection algorithms are intimately connected with robust statistics that down-weight some observations to zero. We define a number of outlier detection algorithms related to the Huber-skip and least trimmed squares estimators, including the one-step Huber-skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse 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.