Reversed preservation of stochastic orders for random minima and maxima with applications

In this paper, reversed preservation properties of right spread order, total time on test order and increasing convex (concave) order when taking random minima and maxima are developed. In this context, reversed preservation properties of some ageing concepts are investigated under parallel (series) systems which are composed of a random number of i.i.d. components. Some applications in reliability and economics are given.     

Ranking opportunity sets in the space of functionings

We develop a ranking of compact, convex and comprehensive opportunity sets defined in the evaluative space of individual functionings. We suppose the existence of a target, that is a multi-dimensional bliss point in terms of functionings. This leads us to define concepts such as essentiality and freedomin a novel way. As a main result, we give an axiomatic characterization of the ranking obtained by minimizing the Euclidean distance between each opportunity set and the target.     

拓扑型极大极小不等式、截口定理和抽象经济平衡点的存在性定理

利用[1]中得到的参数型KKM定理首先证明了区间空间上的几个向量值极大极小定理。应用这些结果,得到了几个拓扑型截口定理和另外三种等价形式,最后讨论了抽象经济平衡点的存在性问题。     

参数型非空交定理和拓扑Riesz空间中的极大极小定理

本文首先证明了区间空间上的几个参数型非空交定理,并由此得到拓扑Riesz空间中的几个新型极大极小定理,本文的结果包含[1、5、6]中主要结果为特例。     

Banach空间的一致极光滑性与平均一致凸性

给出了Ｂａｎａｃｈ空间的很极光滑性、一致极光滑性和平均一致凸Ｂａｎａｃｈ空间之间的关系．     

Do bootstrap confidence procedures behave well uniformly in P?

An important statistical problem is to construct a confidence set for some functional T(P) of some unknown probability distribution P. Typically, this involves approximating the sampling distribution J_n(P) of some pivot based on a sample of size n from P. A bootstrap procedure is to estimate J_n(P) by J_n(&Pcirc;_n), where P?_n is the empirical measure based on a sample of size n from P. Typically, one has that J_n(P) and J_n(P?_n) are close in an appropriate sense. Two questions are addressed in this note. Are J_n(P) and J_n(P?_n) uniformly close as P varies as well? If so, do confidence statements about T(P) possess a corresponding uniformity property? In the case T(P) = P, the answer to the first questions is yes; the answer to the second is no. However, bootstrap confidence statements about T(P) can be made uniform over a restricted, though large, class of P. Similar results apply to other functional T(P).     

关于平均一致凸Banach空间

给出平均一致凸Ｂａｎａｃｈ空间的定义，证明了一致凸Ｂａｎａｃｈ空间是平均一致凸Ｂａｎａｃｈ空间，平均一致凸Ｂａｎａｃｈ空间是自反和弱局部一致凸Ｂａｎａｃｈ空间，并且平均一致凸Ｂａｎａｃｈ空间Ｘ中任意元在Ｘ的闭凸子集中存在唯一的最佳逼近元．     

有非负约束的线性模型

讨论有非负约束的线性模型的估计，证明了此模型可以用矩阵的消去变换来求解，主要应用于可靠性统计分析中。     

On the Distance Between Cumulative Sum Diagram and Its Greatest Convex Minorant for Unequally Spaced Design Points

Abstract.  The supremum difference between the cumulative sum diagram, and its greatest convex minorant (GCM), in case of non-parametric isotonic regression is considered. When the regression function is strictly increasing, and the design points are unequally spaced, but approximate a positive density in even a slow rate ( n ^−1/3), then the difference is shown to shrink in a very rapid (close to n ^−2/3) rate. The result is analogous to the corresponding result in case of a monotone density estimation established by Kiefer and Wolfowitz, but uses entirely different representation. The limit distribution of the GCM as a process on the unit interval is obtained when the design variables are i.i.d. with a positive density. Finally, a pointwise asymptotic normality result is proved for the smooth monotone estimator, obtained by the convolution of a kernel with the classical monotone estimator.