A stochastic algorithm for the recursive approximation of the location θ of a maximum of a regression function has been introduced by Kiefer and Wolfowitz (1952) in the univariate framework, and by Blum (1954) in the multivariate case. The aim of this paper is to provide a companion algorithm to the Kiefer-Wolfowitz-Blum algorithm, which allows to simultaneously recursively approximate the size...

We consider the Kiefer-Wolfowitz (KW) stochastic approximation algorithm and derive general upper bounds on its meansquared error. The bounds are established using an elementary induction argument and phrased directly in the terms of tuning sequences of the algorithm. From this we deduce the nonnecessity of one of the main assumptions imposed on the tuning sequences by Kiefer and Wolfowitz [Kie...

This paper proposes a proof of the convergence distributed and asynchronous version Kiefer-Wolfowitz algorithm where agents do not exchange information with one another.

A nonparametric mixture model approach to empirical Bayes compound decisions for the Gaussian location model is compared with a parametric empirical Bayes approach recently suggested by Martin and Walker and several recent more formal Bayes procedures. Martin and Walker (2013) have recently proposed a parametric empirical Bayes procedure for the classical Gaussian compound decision problem in w...