Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence

The Rényi entropy is a generalisation of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g. consistency, asymptotic normality, and Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g. ε-keys in time series databases and distribution identification problems for dependent samples).     

Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure

The Dirichlet process is a fundamental tool in studying Bayesian nonparametric inference. The Dirichlet process has several sum representations, where each one of these representations highlights some aspects of this important process. In this paper, we use the sum representations of the Dirichlet process to derive explicit expressions that are used to calculate Kolmogorov, Lévy, and Cramér–von Mises distances between the Dirichlet process and its base measure. The derived expressions of the distance are used to select a proper value for the concentration parameter of the Dirichlet process. These tools are also used in a goodness-of-fit test. Illustrative examples and simulation results are included.     

Uniform Tail Asymptotics for the Sum of Two Correlated Classes with Stochastic Returns and Dependent Heavy Tails

Consider a continuous-time risk model with two correlated classes of insurance business and risky investments whose price processes are geometric Lévy processes. By assuming that the correlation comes from a common shock, and the claim sizes are heavy-tailed and pairwise quasi-asymptotically independent, we investigate the tail behavior of the sum of the stochastic present values of the two correlated classes, and a uniform asymptotic formula is obtained.     

伊朗核计划的动因及其影响

自伊朗秘密建造核设施的消息曝光之后,伊朗的核问题成为国际又一热点.本文介绍了伊朗核问题的由来,分析了伊朗现行核政策的意图以及"逆潮流而动"坚持现行核政策的依据,并进一步指出它对未来中东政治格局的影响.     

孙子制胜思想探析

孙子思想体系从内容构成的角度可以分为:孙子的"全胜"思想;孙子的认知规律;孙子的争胜原理。孙子的"全胜"思想是孙子思想的主题,以"不战而屈人之兵"实现目的或目标为其理论目标,追求最"效益"的合理过程为宗旨。孙子的认知规律的核心是"知彼知己"规律,它是孙子知胜和制胜的重要依据和前提。孙子的争胜原理是实现孙子理论宗旨的保障,它衍生于孙子的非对称制胜思想。要获得对抗事件的胜利,必定存在一个非对称的作用,孙子的制胜艺术就是寻找、选择、创造、利用某种非对称作用而获胜的艺术。     

20世纪中国意笔人物画变革纵观

结合20世纪的百年中国社会发展历程背景,以及每阶段中国美术论争的焦点问题,介绍有关中国意笔人物画现代化历程中的重要变革史实,评析中国意笔人物画在内容、形式和技艺发展中的理论和实践,对20世纪中国意笔人物画在不同历史阶段(具体分开创性试验期、探索性发展期和多样化繁荣期三个阶段)中的主要流派及其代表人物,进行分别阐述.     

经济人的过程哲学诠释--社会存在本体论的理论范型

20世纪70年发展起来的社会存在本体论,其实质是关系实在论.人与人之间的首要关系是社会关系.经济关系是社会关系的集中表现.体现经济本质的事件本体论是人的社会存在的元哲学解释.这恰恰是怀特海过程哲学的核心.把社会存在本体论与过程哲学联系起来是使后者走向现代性的正确渠道.21世纪之初,由小科布领军的过程哲学研究正在把这一研究引向深入.     

城市化进程中的城乡协调问题

由于目前在城市化进程中所面临的难题主要是城乡关系的统筹问题.因此,为了实现建立和谐社会的目标,必须采取多项措施进行城乡协调.     

Test for Trend With a Multinomial Outcome

ABSTRACT

There is no established procedure for testing for trend with nominal outcomes that would provide both a global hypothesis test and outcome-specific inference. We derive a simple formula for such a test using a weighted sum of Cochran–Armitage test statistics evaluating the trend in each outcome separately. The test is shown to be equivalent to the score test for multinomial logistic regression, however, the new formulation enables the derivation of a sample size formula and multiplicity-adjusted inference for individual outcomes. The proposed methods are implemented in the R package multiCA.