Consistent estimation of distribution functions under increasing concave and convex stochastic ordering

05/07/2021
by   Alexander Henzi, et al.
0

A random variable Y_1 is said to be smaller than Y_2 in the increasing concave stochastic order if 𝔼[ϕ(Y_1)] ≤𝔼[ϕ(Y_2)] for all increasing concave functions ϕ for which the expected values exist, and smaller than Y_2 in the increasing convex order if 𝔼[ψ(Y_1)] ≤𝔼[ψ(Y_2)] for all increasing convex ψ. This article develops nonparametric estimators for the conditional cumulative distribution functions F_x(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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

10/30/2019

Random concave functions

Spaces of convex and concave functions appear naturally in theory and ap...
06/26/2018

Maximum Likelihood Estimation for Totally Positive Log-Concave Densities

We study nonparametric density estimation for two classes of multivariat...
01/31/2020

Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems

In this paper we study the smooth convex-concave saddle point problem. S...
02/25/2021

On shrinkage estimation of a spherically symmetric distribution for balanced loss functions

We consider the problem of estimating the mean vector θ of a d-dimension...
06/06/2020

Bi-s^*-Concave Distributions

We introduce a new shape-constrained class of distribution functions on ...
06/12/2018

Dynamics of Distributed Updating in Fisher Markets

A major goal in Algorithmic Game Theory is to justify equilibrium concep...
06/29/2021

Active-set algorithms based statistical inference for shape-restricted generalized additive Cox regression models

Recently the shape-restricted inference has gained popularity in statist...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.