The Pitman Inequality For Exchangeable Random Vectors

Authors

J. Behboodian, Shiraz UniversityFollow
Naveen K. Bansal, Marquette UniversityFollow
Gholamhossein Hamedani, Marquette UniversityFollow
Hans Volkmer, University of Wisconsin - Milwaukee

Document Type

Article

Language

eng

Format of Original

5 p.

Publication Date

8-2013

Publisher

Elsevier

Source Publication

Statistics and Probability Letters

Source ISSN

0167-7152

Original Item ID

doi: 10.1016/j.spl.2013.04.010

Abstract

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n) without the assumption of continuity and symmetry for each component X_i:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where all αi≥0 are special weights with ∑i=1nαi=1.

Comments

Statistics and Probability Letters, Vol. 83, No. 8 (August 2013): 1825-1829. DOI. © 2013 Elsevier. Used with permission.

Recommended Citation

Behboodian, J.; Bansal, Naveen K.; Hamedani, Gholamhossein; and Volkmer, Hans, "The Pitman Inequality For Exchangeable Random Vectors" (2013). Mathematics, Statistics and Computer Science Faculty Research and Publications. 164.
https://epublications.marquette.edu/mscs_fac/164