Influence Functions of Halfspace Depth-Based Trimmed Mean and Covariance Matrix

• Activity Number: 692
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jin Wang*
• Companies: Northern Arizona University
• Keywords: influence function ; robustness ; asymptotic distribution ; depth function ; multivariate analysis

Abstract

Although the well-known halfspace depth-based trimmed mean has appeared in the literature for a long time, some issues such as its influence function and asymptotic distribution are still kept open. Investigation on the halfspace depth-based trimmed covariance matrix has not been made yet. Here we derive the influence functions of the halfspace depth-based trimmed mean and covariance matrix. Both influence functions are bounded. The asymptotic distributions of the sample trimmed mean and covariance matrix are obtained via the influence functions.