Exploration of Random Objects through Increasing Ball Statistics

Music City Center 

This work introduces a novel method for exploring object data viewed as random elements in a metric space. The approach evaluates the Fréchet mean of elements within a ball centered at a specific point in the space. We investigate the behaviors of these ball Fréchet means as the ball radius increases, treating them as functional objects dependent on the radius and ball centers. We reduce them into real-valued functions by taking their distance from the global Fréchet mean, thereby enabling the application of traditional functional data analysis techniques. Theoretical results are provided, and the method is illustrated with simulations and applications to human mortality data and U.S. electricity generation data, demonstrating its potential for clustering and outlier detection.

Data exploration

Fréchet mean

Functional data analysis

Object data analysis 

Section on Nonparametric Statistics