A note on confidence intervals for the Kiefer-Wolfowitz problem

A Kiefer – Wolfowitz Comparison Theorem for Wicksell ’ S Problem

We extend the isotonic analysis for 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 useful ...

A Kiefer - Wolfowitz Theorem for Convex Densities

Kiefer and Wolfowitz [14] showed that if F is a strictly curved concave distribution function (corresponding to a strictly monotone density f), then the Maximum Likelihood Estimator F̂n, which is, in fact, the least concave majorant of the empirical distribution function Fn, differs from the empirical distribution function in the uniform norm by no more than a constant times (n logn)2/3 almost s...

A companion for the Kiefer-Wolfowitz-Blum stochastic approximation algorithm

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...

A Kiefer-Wolfowitz algorithm with randomized differences

A Kiefer–Wolfowitz or simultaneous perturbation algorithm that uses either one-sided or two-sided randomized differences and truncations at randomly varying bounds is given in this paper. At each iteration of the algorithm only two observations are required in contrast to 2` observations, where ` is the dimension, in the classical algorithm. The algorithm given here is shown to be convergent un...

A Note on Teaching Binomial Confidence Intervals