Inhomogeneous Markov Chains and Ergodicity Coefficients: John Hajnal (1924–2008)

In 1958, a paper by John Hajnal, a demographer and mathematical statistician, was fundamental in the revival of the theory of inhomogeneous Markov chains. Hajnal made his contribution by the development of tools for the analysis of weak ergodicity, and proofs of fundamental theorems. This article reviews Hajnal's career, and then focuses on the four topics: 1. ergodicity coefficients and the weak ergodicity theorem; 2. scrambling matrices; 3. the coupling theorem; and 4. non-negative matrix products. Related work by other authors, especially Wolfgang Doeblin, is mentioned in context. Attention is given to some recent surveys and applications of ergodicity coefficients, including the Google matrix.     

A simple method for estimating parameters of the location–scale distribution family

The purpose of this paper is to estimate the parameters of the location–scale distribution family. As a special case, the method is used for estimating the parameters of the normal distribution and Cauchy distribution. For the Cauchy distribution, neither the moment estimation method nor the maximum likelihood estimation method works properly for estimating the parameters. The quantiles for obtaining confidence intervals and point estimates for the parameters of the two-parameter Cauchy distribution are given in the paper. It is shown that the estimators obtained in this paper are unbiased with respect to the median and possess some optimal properties.     

农药残留认知与主要影响因素研究——河南省223个小麦种植农户的案例

文章以中国河南省三个不同地区的6个县的223个小麦种植农户为案例,以计划行为理论为主要分析工具,基于结构方程模型研究了影响小麦种植农户农药残留认知的主要因素。研究表明,小麦种植农户的地域、性别、年龄、受教育年限、家庭总人口、农业生产人口、家庭年收入、农药培训、农业技术人员的指导、对小麦安全性的担忧等因素均不同程度地影响其对农药残留的认知。文章的研究发现,小麦种植农户的知觉行为控制、行为态度、主观规范和自身特征因素间的交互作用明显,初步验证了计划行为理论对生产农户的农药残留认知的主要影响因素的研究具有普适性。     

New regression model with four regression structures and computational aspects

A new general class of exponentiated sinh Cauchy regression models for location, scale, and shape parameters is introduced and studied. It may be applied to censored data and used more effectively in survival analysis when compared with the usual models. For censored data, we employ a frequentist analysis for the parameters of the proposed model. Further, for different parameter settings, sample sizes, and censoring percentages, various simulations are performed. The extended regression model is very useful for the analysis of real data and could give more adequate fits than other special regression models.     

On some analogues of lack of memory properties for the Gompertz distribution

We discuss some analogues of the lack of memory property, the strong lack of memory property and the almost lack of memory properties for the Gompertz distribution as applications of the integrated Cauchy functional equation.     

古代中印勾股测望术之比较

勾股测量法是勾股定理的实际应用,在古代中国和印度都曾出现过,而且两国的许多数学著作与天文学著作中都有勾股测量法的记载。两国的勾股测量法由测量太阳高度和晷影长度发展起来,并随着实际问题的需要日益提高。由于社会生活和生产需求的一致,中印两国勾股测量方法存在很多的共性,但都是在各自的本土文化中发展起来的,没有受到外来文化的影响。     

Folk theorems for the observable implications of repeated games

The fact that infinitely repeated games have many different equilibrium outcomes is known as the Folk Theorem. Previous versions of the Folk Theorem have characterized only the payoffs of the game. This paper shows that over a finite portion of an infinitely repeated game, the concept of perfect equilibrium imposes virtually no restrictions on observable behavior. The Prisoner's Dilemma is presented as an example and discussed in detail.I would like to thank an anonymous referee, Sushil Bikhchandani, David Hirshleifer, David Levine, Thomas Voss, and participants in the UCLA Game Theory Seminar for helpful comments.     

关于柯西积分定理的一点注记

讨论具有某种特征映射的类似柯西积分定理的结论 .     

加权改进模糊相似选择方法及其应用

本文对改进模糊相似选择方法作出了进一步的改进,综合权重和海明距离两方面因素,对事物按优劣程度排序,从而更加准确有效,符合实际。     

Heteroscedasticity-robust estimation of autocorrelation

This paper proposes estimators of the first-order autocorrelation that are based on suitably transformed ratios of successive observations. The new estimators are given by simple functions of the observations. Numerical optimization is not required. Simulations show that they are highly robust against extreme values and clusters of high volatility and are therefore particularly useful for the estimation of serial correlation in return series. Besides, the results of the simulation study also call into question the common practice of correcting the small-sample bias of conventional estimators.