On the stability problem for conditional expectation

Wlodzimierz Bryc and Wlodzimierz Smolenski

Statistics & Probability Letters, 1992, vol. 15, issue 1, 41-46

Abstract: The behavior of the conditional expectation Es{;Xvb;Ys}; under a small perturbation Z of the conditioning random variable Y is analyzed. We show that if Y and Z are independent then Es{;Xvb;Y + [var epsilon]Zs}; converges to Es{;Xvb;Ys}; in mean as [var epsilon] --> 0 for all integrable X, provided the distribution of Y is absolutely continuous. We also show that the limit is Es{;Xvb;Y, Zs}; rather than Es{;Xvb;Ys};, i.e., there is no stability, when Y is a discrete (i.e., countably valued) random variable. Finally, we show that in general Es{;Xvb;Y + [var epsilon]Zs}; might have no limit in distribution as [var epsilon] --> 0.

Keywords: Conditional; expectations; stability; perturbation (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(92)90283-B
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:15:y:1992:i:1:p:41-46

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().