Spindles - a hallmark of stage II sleep - are a transient oscillatory phenomenon in the EEG believed to reflect thalamocortical activity contributing to unresponsiveness during sleep. Currently spindles are often classified into two classes: fast spindles, with a frequency of around 14 Hz, occurring in the centro-parietal region; and slow spindles, with a frequency of around 12 Hz, prevalent in...

Upper bounds are given for the distance between the range, matrix range and partition range of a vector measure to the respective convex hulls of these ranges. The bounds are speciied in terms of the maximum atom size, and generalize convexity results of Lyapounov (1940) and Dvoretzky, Wald and Wolfowitz (1951). Applications are given to the bisection problem, the "problem of the Nile", and fai...

A proposal of van der Vaart (1996) for an adaptive estimator of a location parameter from a family of normal scale mixtures is explored. Recent developments in convex optimization have dramatically improved the computational feasibility of the Kiefer and Wolfowitz (1956) nonparametric maximum likelihood estimator for general mixture models and yield an effective strategy for estimating the effi...

Abstract. Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is used to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with some simulation examples as well as ...

We extend the isotonic analysis for the Wicksell’s problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in Astronomy. The main result is a version of the Kiefer-Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n −1 log n faster than n−2/3 log n. The main result is usef...

The paper applies abstract optimisation principles in the space of measures within the context of optimal design problems. It is shown that within this framework it is possible to treat various design criteria and constraints in a unified manner providing a “universal” variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. The described s...