Strong decomposition of random variables

被引：1

作者：

Hoffmann-Jorgensen, Jorgen ^{[1
]}

Kagan, Abram M.

Pitt, Loren D.

Shepp, Lawrence A.

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Aarhus Univ, Dept Math Sci, DK-8000 Aarhus C, Denmark

[3] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[4] Rutgers State Univ, Dept Stat, Piscataway, NJ 08855 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2007年 / 20卷 / 02期

关键词：

absolute continuity; component; Fisher information; singularity;

D O I：

10.1007/s10959-007-0061-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A random variable X is called strongly decomposable into (strong) components Y,Z, if X=Y+Z where Y=phi(X), Z=X-phi(X) are independent nondegenerate random variables and phi is a Borel function. Examples of decomposable and indecomposable random variables are given. It is proved that at least one of the strong components Y and Z of any random variable X is singular. A necessary and sufficient condition is given for a discrete random variable X to be strongly decomposable. Phenomena arising when phi is not Borel are discussed. The Fisher information (on a location parameter) in a strongly decomposable X is necessarily infinite.

引用

页码：211 / 220

页数：10

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