Robust Scale Estimation Under Long-Range Dependence

• Activity Number: 228
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Neville Weber*+ and Garth Tarr and Samuel Mueller
• Companies: University of Sydney and University of Sydney and University of Sydney
• Keywords: Interquartile range ; long range dependence ; robust statistics

Abstract

Over the past twenty years there has been increasing interest in robust statistics and in the behaviour of estimators under long range dependence (LRD). We will consider scale estimators for stationary, zero-mean Gaussian processes in the LRD setting. When the level of dependence is high it is not uncommon to encounter non-normal limiting behaviour for measures of spread such as the standard deviation and Rousseeuw and Croux's robust scale estimator $Q_n,$ a U-quantile statistic, (see L\'{e}vy-Leduc et al., Ann. Statist. (2011)). There has been limited investigation of the behaviour of L-statistics and linear combinations of U-quantiles such as the measure $P_n$ introduced by Tarr et al. (J. Nonparametric Stat.(2012)). The Badhadur representation of sample quantiles under LRD was established by Wu (Ann. Statist. (2005)) and it highlights the more complex behaviour encountered in this case. Wu's result is applied to show that the interquartile range under LRD has similar behaviour to $Q_n.$