A companion for the Kiefer--Wolfowitz--Blum stochastic approximation algorithm

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dc.creatorMokkadem, Abdelkader
dc.creatorPelletier, Mariane
dc.date2006-10-16
dc.date2007-10-23
dc.date.accessioned2026-07-07T08:40:51Z
dc.date.available2026-07-07T08:40:51Z
dc.descriptionA stochastic algorithm for the recursive approximation of the location $θ$ of a maximum of a regression function was introduced by Kiefer and Wolfowitz [Ann. Math. Statist. 23 (1952) 462--466] in the univariate framework, and by Blum [Ann. Math. Statist. 25 (1954) 737--744] in the multivariate case. The aim of this paper is to provide a companion algorithm to the Kiefer--Wolfowitz--Blum algorithm, which allows one to simultaneously recursively approximate the size $μ$ of the maximum of the regression function. A precise study of the joint weak convergence rate of both algorithms is given; it turns out that, unlike the location of the maximum, the size of the maximum can be approximated by an algorithm which converges at the parametric rate. Moreover, averaging leads to an asymptotically efficient algorithm for the approximation of the couple $(θ,μ)$.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053606000001451 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0610487
dc.identifierhttp://arxiv.org/abs/math/0610487
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 4, 1749-1772
dc.identifierdoi:10.1214/009053606000001451
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141494
dc.subjectStatistics Theory
dc.subject62L20 (Primary); 62G08 (Secondary)
dc.titleA companion for the Kiefer--Wolfowitz--Blum stochastic approximation algorithm
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