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Given a sample X 1, …, X n of i.i.d. random variables with common distribution function (df) F and empirical df F n , a statistic S( X 1, …, X n ) is called a statistical functional if it can be written in terms of a functional T, independent of n, such that S( X 1, …, X n ) = T( F n ), for all n ≥ 1. The domain of T contains at least the population df F and the empirical df F n , for all n ≥ 1. In this setting the statistic T( F n ) estimates the parameter T( F).

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Functional Derivatives in Statistics: Asymptotics and Robustness

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  • 发表日期：

    2025年

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  • Luisa Turrin Fernholz

摘要

Given a sample X 1, …, X n of i.i.d. random variables with common distribution function (df) F and empirical df F n , a statistic S( X 1, …, X n ) is called a statistical functional if it can be written in terms of a functional T, independent of n, such that S( X 1, …, X n ) = T( F n ), for all n ≥ 1. The domain of T contains at least the population df F and the empirical df F n , for all n ≥ 1. In this setting the statistic T( F n ) estimates the parameter T( F).