We derive a Monte-Carlo-amenable, minimum variance unbiased estimator of a nonlinear function of a normal mean and the variance of the estimator. Applications to problems arising in the analysis of data measured with error are described. Copyright 2005, Oxford University Press.

It is shown that regression-equivariant high-breakdown estimators necessarily possess the exact-fit property as defined by Yohai and Zamar (1987). Examples are give showing that estimators possessing the exact-fit property can exhibit unusual finite-sample behavior.

We present a variation of the simex algorithm (J. Amer. statist. Assoc. 89 (1994) 1314) appropriate for the case in which the measurement error variance(s) are unknown but replicate measurements are available. The method used pseudo errors generated from random linear contrasts of the observed...

This paper studies the problem of estimating the density of U when only independent copies of X = U + Z is observable where Z is an independent measurement error. Convergence rates of a family of deconvolved kernel density estimators are obtained under different assumptions on the density of Z.

In this paper it is shown that the logistic distribution can be represented as a scale mixture of the standard normal distribution where the mixing density is related to the Kolmogorov--Smirnov distribution. Two derivations of the theorem are presented that give rise to two different...