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2015 Importance accelerated Robbins-Monro recursion with applications to parametric confidence limits
Zdravko I. Botev, Chris J. Lloyd
Electron. J. Statist. 9(2): 2058-2075 (2015). DOI: 10.1214/15-EJS1071


Applying the standard stochastic approximation algorithm of Robbins and Monro (1951) to calculating confidence limits leads to poor efficiency and difficulties in estimating the appropriate governing constants as well as the standard error.

We suggest sampling instead from an alternative importance distribution and modifying the Robbins-Monro recursion accordingly. This can reduce the asymptotic variance by the usual importance sampling factor. It also allows the standard error and optimal step length to be estimated from the simulation. The methodology is applied to computing almost exact confidence limits in a generalised linear model.


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Zdravko I. Botev. Chris J. Lloyd. "Importance accelerated Robbins-Monro recursion with applications to parametric confidence limits." Electron. J. Statist. 9 (2) 2058 - 2075, 2015.


Received: 1 November 2014; Published: 2015
First available in Project Euclid: 17 September 2015

zbMATH: 1327.62177
MathSciNet: MR3397401
Digital Object Identifier: 10.1214/15-EJS1071

Primary: 62F25
Secondary: 65C05

Keywords: confidence limits , generalized linear model , importance sampling , profile upper limits , stochastic approximation

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.9 • No. 2 • 2015
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