On the mathematics of the Jeffreys–Lindley paradox

This paper is concerned with the well known Jeffreys–Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e., the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.     

Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

The use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.     

Several least-squares problems related to the Hodrick–Prescott filtering

The Hodrick–Prescott (HP) filtering is frequently used in macroeconometrics to decompose time series, such as real gross domestic product, into their trend and cyclical components. Because the HP filtering is a basic econometric tool, it is necessary to have a precise understanding of the nature of it. This article contributes to the literature by listing several (penalized) least-squares problems that are related to the HP filtering, three of which are newly introduced in the article, and showing their properties. We also remark on their generalization.     

Some properties of Lin–Wong divergence on the past lifetime data

Measures of statistical divergence are used to assess mutual similarities between distributions of multiple variables through a variety of methodologies including Shannon entropy and Csiszar divergence. Modified measures of statistical divergence are introduced throughout the present article. Those modified measures are related to the Lin–Wong (LW) divergence applied on the past lifetime data. Accordingly, the relationship between Fisher information and the LW divergence measure was explored when applied on the past lifetime data. Throughout this study, a number of relations are proposed between various assessment methods which implement the Jensen–Shannon, Jeffreys, and Hellinger divergence measures. Also, relations between the LW measure and the Kullback–Leibler (KL) measures for past lifetime data were examined. Furthermore, the present study discusses the relationship between the proposed ordering scheme and the distance interval between LW and KL measures under certain conditions.     

Strong law of large numbers and complete convergence for non-identically distributed WOD random variables

In this paper, we establish the strong law of large numbers and complete convergence for non-identically distributed WOD random variables. We derive some new inequalities of Fuk–Nagaev type for the sums of non-identically distributed WD random variables. All these results further extend and refine previous ones.     

应用型高校与企业共建产业学院的优势与困惑

产业学院是应用型高校为服务地方社会经济的发展而与企业深度合作形成的新型办学机构，由高校和企业共同投资，实行理事会领导、院长负责的管理体制，校企协同育人，重视实践教学，组织特征鲜明，办学优势突出。但是，产业学院在发展过程中面临诸多不足：独立法人地位尚未确立，进一步发展缺乏法律保障和依据；现代治理方式和结构尚未建立，具体工作受高校干扰较多，行政化色彩浓厚；运行成本大，缺乏市场化运行机制。为了促进产业学院发展，国家应确立其独立的法律地位，营造发展的政策环境和建立现代化的治理方式与结构；产业学院应建立市场化运行机制，激发面对市场的应变能力，最大限度地发挥自身优势，化解发展过程中的短板。     

The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

比较法视野下我国搜查措施之理论反思

我国有证搜查还处于内部控制、自我约束和事后监督的阶段。被搜查者的合法权利不得不严重依赖于侦查人员搜查的文明程度。而无证搜查立法的拘谨与侦查实践的现实需要之间存在显著的差异。我国搜查措施所存在的问题,显示出搜查措施对侦查机关的规范和约束力度还处于较低的水平,对被搜查者权利的保障仍有所不足。我国不仅需要完善有证搜查制度,而且更需要建立和规范以同意搜查为核心的无证搜查制度,以追随刑事诉讼现代化之步伐,实现法治中国之梦想。     

Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution

A multivariate normal mean–variance mixture based on a Birnbaum–Saunders (NMVMBS) distribution is introduced and several properties of this new distribution are discussed. A new robust non-Gaussian ARCH-type model is proposed in which there exists a relation between the variance of the observations, and the marginal distributions are NMVMBS. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of this normal mean–variance mixture distribution is given. A simulation study and some real data are used to demonstrate the modelling strength of this new model.     

产品服务供应链的“双重收益共享”合作机制

产品与服务融合缓解了"供需错位"矛盾，使得产品服务供应链探索成为"供给侧结构性改革"下供需结构性匹配的重要路径。本文刻画产品服务视角下供应链组织结构的本质特征，构建产品服务供应链合作模型，探讨合作机制下"帕累托改进"区间存在性，揭示合作机制对产品服务供应链效率的作用机理。核心研究发现：供应链多元化组织结构加剧收益分配冲突，并导致服务规模与供应链效率"倒挂"现象，而合作机制下"双重收益共享"合作模型能提升产品服务供应链效率。