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July, 1978 On Asymptotically Efficient Recursive Estimation
Vaclav Fabian
Ann. Statist. 6(4): 854-866 (July, 1978). DOI: 10.1214/aos/1176344259


Stochastic approximation procedures were shown by Sakrison to become asymptotically efficient estimators when used to minimize the Kullback-Leibler information, if certain conditions hold. Further results in this direction were obtained by Nevel'son and Has'minskij. This paper gives, first, alternative conditions for convergence and, secondly, shows that, under weaker conditions, asymptotic optimality is obtained by a modified stochastic approximation procedure. The modified procedure uses a consistent estimate which leads the approximating sequence to a proper local minimum of the Kullback-Leibler information. The conditions under which the procedure is asymptotically optimal are close to or weaker than those for asymptotic optimality of one-step-correction maximum likelihood methods.


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Vaclav Fabian. "On Asymptotically Efficient Recursive Estimation." Ann. Statist. 6 (4) 854 - 866, July, 1978.


Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62031
MathSciNet: MR478506
Digital Object Identifier: 10.1214/aos/1176344259

Primary: 62F10
Secondary: 62F20 , 62L20

Keywords: asymptotically efficient , Fisher bound , maximum likelihood , recursive estimation , stochastic approximation

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 4 • July, 1978
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