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Activity Number: 324
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #318590
Title: Depth Functions and Medians on the Minimal Spanning Tree
Author(s): Reza Modarres*
Companies: The George Washington University
Keywords: Multivariate Median ; Depth function ; Minimal spanning Tree

We represent the observations of a random sample as vertices of a complete weighted graph and propose new depth functions that are applicable to multivariate distributions and data on graphs. We define and compare several depth functions on the minimal spanning tree (MST), including Path, Eccentricity, Peeling, Runt, and Geodesic Convexity depth functions, classify them into four types and study their properties. We consider the corresponding multidimensional medians, investigate their robustness, computational complexity and compare them in a simulation study to find the median vertex under different distributions and sample sizes. An example illustrates the use of the MST-based depth functions.

Authors who are presenting talks have a * after their name.

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