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

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.