箱样条曲面单向凸性条件

本文引入单向凸的概念,给出了箱样条曲面单向凸的必要条件,充分条件。     

关于Schur补和逆M-矩阵问题的进一步讨论

本文继［１］、［２］对Ｓｃｈｕｒ补和逆Ｍ－矩阵进行了讨论,给出了一些结果．     

Dispersive ordering—Some applications and examples

A basic concept for comparing spread among probability distributions is that of dispersive ordering. Let X and Y be two random variables with distribution functions F and G, respectively. Let F ⁻¹ and G ⁻¹ be their right continuous inverses (quantile functions). We say that Y is less dispersed than X (Y≤ _disp X) if G ⁻¹(β)−G ⁻¹(α)≤F ⁻¹(β)−F ⁻¹(α), for all 0<α≤β<1. This means that the difference between any two quantiles of G is smaller than the difference between the corresponding quantiles of F. A consequence of Y≤ _disp X is that |Y ₁−Y ₂| is stochastically smaller than |X ₁−X ₂| and this in turn implies var(Y)≤var(X) as well as E[|Y ₁−Y ₂|]≤E[|X ₁−X ₂|], where X ₁, X ₂ (Y ₁, Y ₂) are two independent copies of X(Y). In this review paper, we give several examples and applications of dispersive ordering in statistics. Examples include those related to order statistics, spacings, convolution of non-identically distributed random variables and epoch times of non-homogeneous Poisson processes. This work was supported in part by KOSEF through Statistical Research Center for Complex Systems at Seoul National University. Subhash Kochar is thankful to Dr. B. Khaledi for many helpful discussions.     

Measuring cross-country technological catch-up through variable-parameter FDH

In this paper, we estimate indices of technological catch-up for a sample of 52 countries through the FDH approach with variable scaling parameters proposed in Kerstens and Vanden Eeckaut (1999). We show that this technique has significant advantages for the international comparisons of productivity and, more generally, wherever the assumption of convexity for the production set is not likely to be appropriate. We want to thank Laurens Cherchye, Hal Fried, Kristian Kerstens and an anonymous referee for useful comments on preceding versions of this paper. The usual disclaimer applies. Financial support from the MURST, Italy, is gratefully acknowledged.     

All Invariant Moments of the Wishart Distribution

Abstract.  In this paper, we compute moments of a Wishart matrix variate U of the form E ( Q ( U )) where Q ( u ) is a polynomial with respect to the entries of the symmetric matrix u , invariant in the sense that it depends only on the eigenvalues of the matrix u . This gives us in particular the expected value of any power of the Wishart matrix U or its inverse U ^{− 1}. For our proofs, we do not rely on traditional combinatorial methods but rather on the interplay between two bases of the space of invariant polynomials in U . This means that all moments can be obtained through the multiplication of three matrices with known entries. Practically, the moments are obtained by computer with an extremely simple Maple program.     

Convexity and Differentiability of Controlled Risk

We investigate risk associated with the violation of a constraint, which is desirable but hardly satisfiable in all possible states of nature.     

Stochastic Orderings of Order Statistics of Independent Random Variables with Different Scale Parameters

This is an article on recent results on stochastic comparisons of order statistics of n independent random variables differing in their scale parameters. Most of the results obtained so far are for the Weibull and the Gamma distributions.     

Testing uniformity for the case of a planar unknown support

A new test is proposed for the hypothesis of uniformity on bi‐dimensional supports. The procedure is an adaptation of the “distance to boundary test” (DB test) proposed in Berrendero, Cuevas, & Vázquez‐Grande (2006). This new version of the DB test, called DBU test, allows us (as a novel, interesting feature) to deal with the case where the support S of the underlying distribution is unknown. This means that S is not specified in the null hypothesis so that, in fact, we test the null hypothesis that the underlying distribution is uniform on some support S belonging to a given class ${\cal C}$ . We pay special attention to the case that ${\cal C}$ is either the class of compact convex supports or the (broader) class of compact λ‐convex supports (also called r‐convex or α‐convex in the literature). The basic idea is to apply the DB test in a sort of plug‐in version, where the support S is approximated by using methods of set estimation. The DBU method is analysed from both the theoretical and practical point of view, via some asymptotic results and a simulation study, respectively. The Canadian Journal of Statistics 40: 378–395; 2012 © 2012 Statistical Society of Canada     

Sur la convergence des tests de Schlee et de Yatchew

L'auteur adapte l'approche de Schlee (1980) et de Yatchew (1992) à la construction de deux tests de convexité pour une fonction de régression dans un modèle non paramétrique. Il établit de nouveaux résultats de convergence pour ces tests et étudie leur comportement dans de petits échantillons à l'aide de simulations.     

Some recent results for series system reliability

Asymptotic properties of key test results ate obtained. Some further results on the Lindstrom-Madden method are given, including a binomial-Poisson inequality, together with some numerical examples. Simplified proofs of some results of Pledger and Proschan (1971) and Nevius, Proschan and Sethuraman (1977) are provided and the listing of a FORTRAN program to calculate a lower bound to the 1-α lower confidence limit on the system reliability is given.