Abstract
A random variable Y1 is said to be smaller than Y2 in the increasing concave stochastic order if for all increasing concave functions
for which the expected values exist, and smaller than Y2 in the increasing convex order if
for all increasing convex ψ. This article develops nonparametric estimators for the conditional cumulative distribution functions
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
and for continuously distributed X.
Supplementary Materials
Proofs and additional figures:Proofs of the theoretical results in Sections 2 and 3, and additional figures for the simulation study in Section 5. (.pdf file)
Code and replication material:R code implementing the estimators, and replication material for the simulations and case study. (.zip file)
Disclosure Statement
The authors report there are no competing interests to declare.
Acknowledgments
The author is grateful to Johanna Ziegel and Timo Dimitriadis for helpful comments and discussions. Many useful comments by the editor, the associate editor and anonymous referees have helped to improve this article.