Strong Limit Theorems for Pairwise NQD Random Variables

A number of strong laws of large numbers for sequences of pairwise negative quadrant dependent (NQD) random variables have been established by using the generalized three series theorem. In this article, we obtain a strong law of large numbers by using the truncation technique and method of subsequences instead of the generalized three series theorem. Our result generalizes and improves on the corresponding one in Li and Yang (2008 Li , R. , Yang , W. ( 2008 ). Strong convergence of pairwise NQD random sequences . J. Math. Anal. Appl. 344 : 741 – 747 .[Crossref], [Web of Science ®] , [Google Scholar]). We also obtain a complete convergence result for an array of rowwise pairwise NQD random variables.     

Some results following from conditional characteristic functions

ABSTRACT

The purpose of this article is to derive rigorously some results following from conditional characteristic functions and anticipate that they will prove to be of significant applicability. Specifically, Khintchine weak law of large numbers, Lévy central limit theorem, inversion theorem, uniqueness theorem, characterization of identical distribution, and characterization of independence are all generalized to conditional setup.     

New ASA Fellows—1967

This paper presents at an elementary level a unified presentation of concepts related to sufficiency and minimal sufficiency. Extensively discussed are techniques for showing in a particular statistical model that a given statistic is not sufficient or that a given sufficient statistic is not minimal. The applicability of these techniques is illustrated in three examples.     

Convergence rates in the law of large numbers for END linear processes with random coefficients

Abstract

In this paper, we consider convergence rates in the Marcinkiewicz–Zygmund law of the large numbers for the END linear processes with random coefficients. We extend some results of Baum and Katz (1965 Baum, L. E., and M. Katz. 1965. Convergence rates in the law of large numbers. Transactions of the American Mathematical Society 120 (1):108–23. doi: 10.2307/1994170.[Crossref], [Web of Science ®] , [Google Scholar]) to the case of dependent linear processes with the random coefficients.     

收益为模糊的区间指派博弈的Owen值

Owen值是合作博弈中比较重要的一种解,而指派博弈恰好是Owen值在现实中的应用。鉴此,提出一类具有模糊收益值的区间指派博弈,并利用区间数的相关理论,在通过建立公理化体系对区间指派博弈的Owen值进行研究的同时,给出一个算例分析并验证其正确性。     

基于投影的直觉模糊数多属性决策方法

针对指标取值以直觉模糊数形式给出的多属性决策问题,提出了一种基于投影的直觉模糊决策方法.该方法依据一般投影分析方法的基本思路,给出了解决属性取值为直觉模糊数的多属性决策问题的计算步骤,其核心是通过构建并求解每个方案在虚拟正、负理想方案上的投影,进而计算出每个方案对虚拟正、负理想方案的相对隶属度,即可得到所有方案的排序结果.最后给出的数值算例表明,该方法简单、有效和易于计算.     

等差数列拟阵及其应用

首次提出"等差数列拟阵"、"等差数列参数系"、"幂等相似矩阵方程"、"行序"及"倒序"、"优美矩 阵"等概念,并探讨了"等差数列拟矩阵"的一些性质及应用例子。同时提出了两个开问题。     

Estimation of the Population Size in the Classical Occupancy Problem

In the classical occupancy problem where the random variable X is the number of N elements selected by K individuals when each element is equally likely to be chosen by any of the individuals, it is desired to estimate N. Three estimators given in the literature are compared with three estimators derived in this article, two of which are based on Bayesian methods, utilizing a simulation study. One of the Bayes estimators appears to perform the best along with one proposed in the literature in 1968. The estimators are also compared using data obtained from a cemetery in Ohio.