Some New Results on Likelihood Ratio Orderings for Spacings of Heterogeneous Exponential Random Variables

Let X ₁, X ₂,…, X _n be independent exponential random variables with X _i having failure rate λ _i for i = 1,…, n. Denote by D _i:n  = X _i:n  ? X _i?1:n the ith spacing of the order statistics X _1:n  ≤ X _2:n  ≤ ··· ≤ X _n:n , i = 1,…, n, where X _0:n ≡ 0. It is shown that if λ _n+1 ≤ [≥] λ _k for k = 1,…, n then D _n:n  ≤ _lr D _n+1:n+1 and D _1:n  ≤ _lr D _2:n+1 [D _2:n+1 ≤ _lr D _2:n ], and that if λ _i  + λ _j  ≥ λ _k for all distinct i,j, and k then D _n?1:n  ≤ _lr D _n:n and D _n:n+1 ≤ _lr D _n:n , where ≤ _lr denotes the likelihood ratio order. We also prove that D _1:n  ≤ _lr D _2:n for n ≥ 2 and D _2:3 ≤ _lr D _3:3 for all λ _i 's.     

Characterizations of the poisson process using,the variance

Let γ(t) be the residual life at time t of the renewal process {A(t), t > 0}, which has F as the common distribution function of the inter-arrival times. In this article we prove that if Var(γ(t)) is constant, then F will be exponentially or geometrically distributed under the assumption F is continuous or discrete respectively. An application and a related example also are given.     

青岛一套表的实践与经验

 企业统计一套表一直是统计制度方法改革和实践中的焦点问题。本文通过对青岛市统计局企业一套表制度实施情况的案例分析,系统界定了企业一套表的概念和内涵,全面展现了企业一套表的运作过程,客观分析了制约企业一套表实施的主要原因,并提出了在现阶段实施企业统计一套表的条件和要求。     

Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface

In many situations the diagnostic decision is not limited to a binary choice. Binary statistical tools such as receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) need to be expanded to address three-category classification problem. Previous authors have suggest various ways to model the extension of AUC but not the ROC surface. Only simple parametric approaches are proposed for modeling the ROC measure under the assumption that test results all follow normal distributions. We study the estimation methods of three-dimensional ROC surfaces with nonparametric and semiparametric estimators. Asymptotical results are provided as a basis for statistical inference. Simulation studies are performed to assess the validity of our proposed methods in finite samples. We consider an Alzheimer's disease example from a clinical study in the US as an illustration. The nonparametric and semiparametric modelling approaches for the three way ROC analysis can be readily generalized to diagnostic problems with more than three classes.     

A likelihood based estimator for vector autoregressive processes

A onestep estimator, which is an approximation to the unconditional maximum likelihood estimator (MLE) of the coefficient matrices of a Gaussian vector autoregressive process is presented. The onestep estimator is easy to compute and can be computed using standard software. Unlike the computation of the unconditional MLE, the computation of the onestep estimator does not require any iterative optimization and the computation is numerically stable. In finite samples the onestep estimator generally has smaller mean square error than the ordinary least squares estimator. In a simple model, where the unconditional MLE can be computed, numerical investigation shows that the onestep estimator is slightly worse than the unconditional MLE in terms of mean square error but superior to the ordinary least squares estimator. The limiting distribution of the onestep estimator for processes with some unit roots is derived.     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

浅析水墨动画片的空间意识

水墨动画是中国传统水墨画与动画技术相结合的颇具民族特色的一种动画片种.它将中国传统水墨画的题材、笔墨节奏、审美空间意识引入到动画制作中,呈现"动画化"的水墨艺术.本文首先分析了传统水墨画所表现的节奏化自然、"阴阳"、"有无"的空间意识,再从属于电影范畴的水墨动画片的视听语言角度来阐述水墨艺术仅仅"动起来"还不够,还要达到真正意义上的"动画化",才能表现出比传统水墨画更有意蕴的空间意识.     

水族习惯法及其变迁——以贵州省三都水族自治县塘党寨为例

本文通过对贵州省三都水族自治县的一个典型水族村寨——恒丰乡塘党寨——的田野调查,描述了水族习惯法的表现形式、维护机制及其变迁。文章认为,水族地区社会经济的发展、国家权力的深入、长期的“送法下乡”活动以及宗教信仰等文化背景的深刻变化,是水族习惯法发生变迁的主要原因。研究这些变迁及其原因,对于理解和认识少数民族地区乃至整个农村的法治建设,具有不可忽视的作用。     

民族地区干部如何看待民族地区加快发展问题--云南地方干部问卷调查分析报告

新世纪中国民族地区面临的最大机遇是社会发展指标追赶的机遇,面临的最大挑战是人类贫困,从而使民族地区传统发展战略和宏观管理政策将面临着严峻的挑战。因此,本文依据具有民族地区代表性的云南地方干部调查问卷统计分析结果,通过考察民族地区发展战略的制定者和宏观管理政策的执行者——民族地区干部——对民族地区加快发展问题的认识和理解,总结出了一些有益的政策启示。