Statistics Papers

Document Type

Journal Article

Date of this Version

1991

Publication Source

The Annals of Probability

Volume

19

Issue

4

Start Page

1781

Last Page

1797

DOI

10.1214/aop/1176990236

Abstract

We show that if f is a probability density on Rn wrt Lebesgue measure (or any absolutely continuous measure) and 0 ≤ f ≤ 1, then there is another density g with only the values 0 and 1 and with the same (n−1)-dimensional marginals in any finite number of directions. This sharpens, unifies and extends the results of Lorentz and of Kellerer.

Given a pair of independent random variables 0 ≤ X, Y ≤ 1, we further study functions 0 ≤ ϕ ≤ 1 such that Z = ϕ (X,Y) satisfies E(Z|X) = X and E(Z|Y) = Y. If there is a solution then there also is a nondecreasing solution ϕ(x,y). These results are applied to tomography and baseball.

Keywords

baseball, tomography, marginals

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Date Posted: 27 November 2017

This document has been peer reviewed.