Depth-Based Statistical Methods for Random Graphs

• Activity Number: 66
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ricardo Fraiman*
• Companies: Universidad de la República
• Keywords: random graphs, depths, principal components

Abstract

The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, statistical analysis of graph sequences is less developed. In this paper we focus on graphs with a fixed number of labeled nodes and study some statistical problems in a nonparametric framework. We introduce natural notions of center and a depth function for graphs that evolve in time. This allows us to develop several statistical techniques including testing, supervised and unsupervised classification, and a notion of principal component sets in the space of graphs. Some examples and asymptotic results are given, as well as a real data example.