Sharp upper mean-variance bounds for trimmed means from restricted families

We apply the method of projection to derive sharp upper mean-variance bounds on trimmed means of order statistics of i.i.d. samples coming from restricted families of probability measures. Two families are considered: distributions with decreasing density and decreasing failure rate. We also present some numerical results.     

Characterization of an optimal matrix estimator under convex loss function

Characterization of an optimal vector estimator and an optimal matrix estimator are obtained. In each case appropriate convex loss functions are considered. The results are illustrated through the problems of simultaneous unbiased estimation, simultaneous equivariant estimation and simultaneous unbiased prediction. Further an optimality criterion is proposed for matrix unbiased estimation and it is shown that the matrix unbiased estimation of a matrix parametric function and the minimum variance unbiased estimation of its components are equivalent.     

Maximally even sets and configurations: common threads in mathematics,physics, and music

Convex (concave) interaction weighting functions are combined with circular configurations of black and white sites to determine configurations that have minimum (maximum) weight. These configurations are called maximally even configurations. It is shown that for a given number of black and white sites, all maximally even configurations are equivalent under rotation and reflection, and a simple algorithm is constructed that generates these configurations. A number of equivalent conditions that determine a maximally even configuration are established. These equivalent conditions permit maximally even configurations to apply to a number of seemingly disparate problems including the dinner table and concentric circles problems, the one-dimensional antiferromagnetic Ising model, and musical scales. This paper is dedicated to the memory of John Clough (1928–2003). Without his seminal works in music theory and patient encouragement of others, this work and much of the work referenced herein would never have been started, much less completed. The field of mathematical music theory owes a great debt to John Clough. The authors are privileged to have known and worked with John Clough.     

Nonparametric tests for strictly increasing virtual valuations

This paper shows that for absolutely continuous valuation distributions the increasing virtual valuations is equivalent to the increasing odds rate. Based on this new characterization we develop two nonparametric tests for the strictly increasing virtual valuations by using the generalized total time on test transform. The empirical type I error rate and power performance of the two tests are examined through Monte Carlo simulations. As illustrations the two tests are also applied to two real data sets collected from eBay.     

框式凸规划的原—对偶仿射尺度算法

文章对框式凸规划问题设计了一个原—对偶仿射尺度算法 ,证明该算法的迭代复杂性为多项式时间性     

The convex hull of a dependent vector-valued process

An important problem in the study of animal behaviour is the determination of home range. This set can be estimated by the convex hull of the location of an animal at successive time points. However, this estimate is based on a sample of highly dependent observations when the time intervals between fixes are small. In this paper we quantify the effect of dependence on various properties of the convex hull of several dependent point processes in the plane using Monte-Carlo methods. We compare our results with the independent case and make some comments on the asymptotic behaviour of this set.     

EF-based strategies for productivity improvements at wet-etch stations

Abstract

In complex manufacturing environments, Cycle Time (CT) reductions obtained at critical production steps could generate considerable productivity improvements and lead to capacity increases at no investment costs. A wet-etch station operating in a real semiconductor manufacturing plant has been modelled to investigate the impact of different assignment strategies on CT performance. Assignment strategies based on the “Earliest Finish” (EF) concept have been developed and their productivity efficiency compared with a workload balance-based strategy. The EF-based strategies differ from each other for both computational complexity and amount of real-time information required. Encouraging results obtained for a high detail level EF strategy have inspired the development of conceptually similar strategies characterised by reduced implementation efforts. Fundamental implementation constraints, suggested by the manufacturing engineers familiar with the wet-etch station, have been taken into account throughout the different stages of this study. CT reductions ranging between 11% and 28% could be achieved at the modelled wet-etch station.     

MVE, MCD, and MZE: A simulation study comparing convex body minimizers

Summary: In a recent work (Paris Scholz, 2002), a new robust estimator for convex bodies has been proposed, based on the estimation of a zonoid of a distribution. This so–called minimum volume zonoid estimator (MZE) is similar in type to the well–known robust approaches of the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD), all three seeking for a subset of given data for which some criteria are minimized. We investigate the similarity between these three concepts by comparing which subsets are chosen to be the optimal ones.