A Newton-Raphson Version of the Multivariate Robbins-Monro Procedure

The continuous dynamic Robbins-Monro procedure

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...

A Robbins-Monro type learning algorithm for an entropy maximizing version of stochastic Optimality Theory

The object of the present work is the analysis of the convergence behaviour of a learning algorithm for grammars belonging to a special version – the maximum entropy version – of stochastic Optimality Theory. Stochastic Optimality Theory is like its deterministic predecessor, namely Optimality Theory as introduced by Prince and Smolensky, in that both are theories of universal grammar in the se...

Higher Order Representations of the Robbins – Monro Process

For quasi–linear regression functions the Robbins–Monro process Xn is decomposed in a sum of a linear form and a quadratic form both defined in the observation errors. Under regularity conditions the remainder term is of order O(n−3/2) with respect to the Lp-Norm. If a cubic form is added, the remainder term can be improved up to an order of O(n−2). As a corollary the expectation of Xn is expan...

@bullet Estimation following a Robbins-monro Designed Experiment