B1277
Title: Empirical processes on trees and applications to depth functions
Authors: Giacomo Francisci - George Mason University (United States) [presenting]
Anand Vidyashankar - George Mason University (United States)
Abstract: The asymptotic behavior of empirical processes for tree-indexed random variables over a class of functions F is investigated. Specifically, under suitable measurability and moment assumptions, sufficient conditions are provided for the uniform law of large numbers (LLN) and the uniform central limit theorem in terms of random metric entropy. Additionally, we establish the uniform rates of convergence for the LLN. These results allow the development of the asymptotic properties of Tukey halfspace depth when F is the class of indicators of halfspaces facilitating an inquiry concerning medians and quantiles of tree-indexed random variables.
