Data Depth for Statistically Equivalent Blocks

• Activity Number: 245
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Reza Modarres*+ and Zhenyu Liu
• Companies: The George Washington University and The George Washington University
• Keywords: Statisticallly Equivalent Blocks ; Data Depth ; Nonparametric Analysis ; Distribution Function

Abstract

Given a random sample of random vectors, statistically equivalent blocks (SEB) can be constructed using a sequence of cutting functions to provide a relative ordering of the vectors. However, the existing cutting functions in the literature are mostly component-wise to facilitate presentation and the resulting SEBs have pre-specified shapes. We explore the construction of SEBs based on data depth (DSEB) and their application. DSEBs are data driven, center-outward layers of shells whose shape reflects the underlying geometric features of the unknown DF. We propose a control quantile test based on DSEBs for testing the equality of two distribution function in a multivariate setting. The proposed statistic is distribution free under the null hypothesis. We show that the proposed test is powerful in detecting the differences in location, scale and shape (skewness or kurtosis) changes.