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Started by druck Dennis W. Ruck
Thu, 29 Oct 1992 17:28
Mean Square Convergence: A Necessary Condition?
Author: druck Dennis W. Ruck
Date: Thu, 29 Oct 1992 17:28
Date: Thu, 29 Oct 1992 17:28
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I am interested in mean square convergence as it applies to random variables.
My specific query is this:
Given: Let X_n n=1,2,3,... and X be random variables. And suppose that the
sequence X_n converges in mean square to X, that is
lim_(n->infinite) E{ (X_n - X)^2 } = 0
Hypothesis: lim_(n->infinite) E{ X_n } = E{ X }
I am not sure this is true or under what conditions it might be true. I would
appreciate any enlightenment on this matter you can provide. I have searched
books by Papoulis, Shanmugan, W. Gardner, and Davenport without success.
Please reply directly (I do not normally read this newsgroup). If there is
sufficient interest, I will summarize to the net. Thanks!
--
Dennis W. Ruck Air Force Institute of Technology
druck@afit.af.mil Wright-Patterson AFB, Ohio
(NeXTmail Welcome)
Re: Mean Square Convergence: A Necessary Condition?
Author: Michi Hauser
Date: Fri, 06 Nov 1992 18:49
Date: Fri, 06 Nov 1992 18:49
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-- Michael Hauser University of Economics and Business Adminstration Department for Applied Statistics and Data Processing Augasse 2-6, 1090 Vienna, Austria Tel. *43/1/31336 4759 email: hauser@wu-wien.ac.at Spanos,A.(1986): Statistical foundations of econometric modelling, Cambridge Univ. press, p.190, Chp. Introduction to asymptotic theory : If X_n converges in the r-th mean to X for some r>=1 then X_n converges in the l-th mean to X for 0<l<r. Your r=2 and l=1 . Best wishes Michael
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