Nonparametric Inference for Location Parameters via Fréchet Functions

Abstract

Given a random object on a stratified space, one defines the Fréchet mean, the Fréchet antimean and additional population parameters associated withits Fréchet function, in case this function is a Morse function as well. In this paper we give large sample and nonparametric bootstrap estimation methods for these parameters, followed by the consistency of Fréchet sample antimean and the Central Limit Theorem of Fréchet sample antimean.