Efficient Robbins--Monro procedure for binary data

The Robbins--Monro procedure does not perform well in the estimation of extreme quantiles, because the procedure is implemented using asymptotic results, which are not suitable for binary data. Here we propose a modification of the Robbins--Monro procedure and derive the optimal procedure for binary data under some reasonable approximations. The improvement obtained by using the optimal procedure for the estimation of extreme quantiles is substantial. Copyright Biometrika Trust 2004, Oxford University Press.