Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

TY - JOUR

T1 - Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

AU - Johansen, Søren

AU - Nielsen, Bent

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

U2 - 10.1111/sjos.12174

DO - 10.1111/sjos.12174

M3 - Journal article

SN - 0303-6898

VL - 43

SP - 321

EP - 348

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

IS - 2

ER -