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

Bibliographic Data

ID19418797
AuthorsAlexander Henzi (0000-0001-5995-0543, University of Bern, Bern, Switzerland, corresponding author)
Year2023
Volume41
Issue4
Pages1203-1214
Publication date2023-10-02
Open AccessNo
TypeARTICLE
VenueJournal of Business and Economic Statistics (JOURNAL)
Journal identifiersISSN: 0735-0015 • E-ISSN: 1537-2707
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/07350015.2022.2116026
OpenAlexW3162067151
LanguageEN
References cited36

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

Combinatorics · Concave function · Covariate · Cumulative distribution function · Discrete mathematics · Estimator · Geometry · Mathematical analysis · Nonparametric statistics · Probability density function · Random variable · Regular polygon · Statistics · Stochastic ordering · Strong consistency · Bayesian Methods and Mixture Models · Mathematics · Statistical Methods and Bayesian Inference · Statistical Methods and Inference

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