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The optimal linear combination of control variates in the presence of asymptotically negligible bias
Author(s) -
Glynn Peter W.,
Iglehart Donald L.
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198910)36:5<683::aid-nav3220360512>3.0.co;2-l
Subject(s) - mathematics , asymptotically optimal algorithm , control variates , sample size determination , optimal control , constant (computer programming) , mean squared error , linear model , statistics , sample (material) , unbiased estimation , mathematical optimization , computer science , monte carlo method , estimator , hybrid monte carlo , chemistry , chromatography , markov chain monte carlo , programming language
The optimal linear combination of control variates is well known when the controls are assumed to be unbiased. We derive here the optimal linear combination of controls in the situation where asymptotically negligible bias is present. The small‐sample linear control which minimizes the mean square error (MSE) is derived. When the optimal asymptotic linear control is used rather than the optimal small‐sample control, the degradation in MSE is c/n 3 , where n is the sample size and c is a known constant. This analysis is particulary relevant to the small‐sample theory for control variates as applied to the steady‐state estimation problem. Results for the method of multiple estimates are also given.