Recently, Sargent and Shanthikumar [5] developed an interesting new variance reduction technique designed to exploit the stochastic structure associated with a cyclic regenerative process. Our purpose here is to study precise conditions under which the confidence intervals proposed in [5] are asymptotically valid. This analysis will provide us with the side benefit of obtaining an optimal way o...

The authors consider the problem of estimating, under quadratic loss, the mean of a spherically symmetric distribution when its norm is supposed to be known and when a residual vector is available. They give a necessary and sufficient condition for the optimal James-Stein estimator to dominate the usual estimator. Various examples are given that are not necessarily variance mixtures of normal d...

Analysis of variance (ANOVA) is one of the most frequently used statistical methods in medical research. The need for ANOVA arises from the error of alpha level inflation, which increases Type 1 error probability (false positive) and is caused by multiple comparisons. ANOVA uses the statistic F, which is the ratio of between and within group variances. The main interest of analysis is focused o...

A common class of shielding problems involves the calculation of biological dose rates from large distributed sources at localised positions. A typical example is that of calculating the dose at points around a transport cask. Sophisticated variance reduction methods must be used in Monte Carlo calculations to sample from the important parts of the source and to propagate particles towards the ...

In this paper we propose a methodology for minimizing the variance of a cube (mosaicked) representation of a scene imaged by a pan-tilt camera. The minimization is based on the estimation of the vignetting image distortion, using the pan and tilt degrees of freedom instead of color calibrating patterns. Experiments with real images show that variance minimization is effective for improving even...

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of populations tends to infinity. We consider several cases of various orders of the sample sizes and show that the maximum likelihood estimator of the variance may or m...

We introduce a new version of Stein’s method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance has to be bounded has an explicit formula that makes it possible to carry out the program more easily. As an applicatio...