Electronic Journal of Statistics

Importance accelerated Robbins-Monro recursion with applications to parametric confidence limits

Zdravko I. Botev and Chris J. Lloyd

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Abstract

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.

Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2058-2075.

Dates
Received: November 2014
First available in Project Euclid: 17 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1442513544

Digital Object Identifier
doi:10.1214/15-EJS1071

Mathematical Reviews number (MathSciNet)
MR3397401

Zentralblatt MATH identifier
1327.62177

Subjects
Primary: 62F25: Tolerance and confidence regions
Secondary: 65C05: Monte Carlo methods

Keywords
Stochastic approximation generalized linear model confidence limits profile upper limits importance sampling

Citation

Botev, Zdravko I.; Lloyd, Chris J. Importance accelerated Robbins-Monro recursion with applications to parametric confidence limits. Electron. J. Statist. 9 (2015), no. 2, 2058--2075. doi:10.1214/15-EJS1071. https://projecteuclid.org/euclid.ejs/1442513544


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