Consistent Estimation of Distribution Functions under Increasing Concave and Convex Stochastic Ordering

Alexander Henzi

Journal of Business & Economic Statistics, 2023, vol. 41, issue 4, 1203-1214

Abstract: A random variable Y1 is said to be smaller than Y2 in the increasing concave stochastic order if E[ϕ(Y1)]≤E[ϕ(Y2)] for all increasing concave functions ϕ for which the expected values exist, and smaller than Y2 in the increasing convex order if E[ψ(Y1)]≤E[ψ(Y2)] for all increasing convex ψ. This article develops nonparametric estimators for the conditional cumulative distribution functions Fx(y)=ℙ(Y≤y|X=x) of a response variable Y given a covariate X, solely under the assumption that the conditional distributions are increasing in x in the increasing concave or increasing convex order. Uniform consistency and rates of convergence are established both for the K-sample case X∈{1,…,K} and for continuously distributed X.

Date: 2023
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DOI: 10.1080/07350015.2022.2116026

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