A note on characterization based on shannon entropy of record statistics

In this note we compare the Shannon entropy of record statistics with the Shannon entropy of the original data and give an application to characterization of the generalized Pareto distribution,     

Universal codes as a basis for time series testing

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.     

熵权双基点法在网络广告效果评估中的应用

文章运用熵权双基点法,对网络广告的社会效果进行了评估。双基点法在一定程度上解决了单方面基于理想点或负理想点进行决策时,未能充分利用已知信息,因而产生偏差的问题,使决策更贴近于实际。     

基于管理熵模型的外部因素评价矩阵重构

基于企业外部系统的复杂性,运用管理熵和管理耗散理论,重构企业的外部因素评价矩阵。通过计算企业外部系统使企业产生的外部管理熵流值,并考虑各外部子系统的相互影响力,以度量企业外部系统对企业的综合影响力,评价企业现行战略对外部系统的适应性。     

基于信息熵与Rough集理论的城市信息系统知识依赖度分析

以城市信息化空间数据处理为研究背景,基于信息熵与Rough集理论解决信息系统中信息不确定、数据量大的困难。从Rough集的基本概念出发,给出决策表的知识表达系统,探讨了信息熵处理知识依赖度的方法。最后通过运用该方法对城市空间数据决策表的实例进行属性值依赖关系的确定。     

Quasi-universal bandwidth selection for kernel density estimators

Let f?_n, h denote the kernel density estimate based on a sample of size n drawn from an unknown density f. Using techniques from L₂ projection density estimators, the author shows how to construct a data-driven estimator f?_n, h which satisfies This paper is inspired by work of Stone (1984), Devroye and Lugosi (1996) and Birge and Massart (1997).     

灰聚类分析结果灰性的测度

在引入了灰聚类权序列的熵的基础上,指出了灰聚类分析结果与聚类权序列熵的关系。给出了灰聚类分析结果灰性测度方法,并研究了此灰生测度的性质。灰聚类分析结果灰性的量化能够帮助应用者深入认识灰聚类分析的结果。通过实例进一步阐明了计算灰聚类分析结果灰性测度的步骤和实际意义。     

产品开发价值比较研究

本文通过对产品开发筛选环节的分析,提出了产品开发价值比较研究的问题;在对熵权法用于产品开发价值比较研究的可行性进行充分论证的基础上,运用熵权法及层次分析法对产品开发价值进行了比较研究;继而对运用熵权法和层次分析法进行产品开发价值比较研究的结果进行了分析;并讨论将熵权法和层次分析法同时应用对产品构思筛选准确性的影响,旨在寻求更科学的对产品构思进行筛选的方法。     

Asymptotic behaviour and statistical applications of divergence measures in multinomial populations: a unified study

Divergence measures play an important role in statistical theory, especially in large sample theories of estimation and testing. The underlying reason is that they are indices of statistical distance between probability distributions P and Q; the smaller these indices are the harder it is to discriminate between P and Q. Many divergence measures have been proposed since the publication of the paper of Kullback and Leibler (1951). Renyi (1961) gave the first generalization of Kullback-Leibler divergence, Jeffreys (1946) defined the J-divergences, Burbea and Rao (1982) introduced the R-divergences, Sharma and Mittal (1977) the (r,s)-divergences, Csiszar (1967) the ϕ-divergences, Taneja (1989) the generalized J-divergences and the generalized R-divergences and so on. In order to do a unified study of their statistical properties, here we propose a generalized divergence, called (h,ϕ)-divergence, which include as particular cases the above mentioned divergence measures. Under different assumptions, it is shown that the asymptotic distributions of the (h,ϕ)-divergence statistics are either normal or chi square. The chi square and the likelihood ratio test statistics are particular cases of the (h,ϕ)-divergence test statistics considered. From the previous results, asymptotic distributions of entropy statistics are derived too. Applications to testing statistical hypothesis in multinomial populations are given. The Pitman and Bahadur efficiencies of tests of goodness of fit and independence based on these statistics are obtained. To finish, apendices with the asymptotic variances of many well known divergence and entropy statistics are presented. The research in this paper was supported in part by DGICYT Grants N. PB91-0387 and N. PB91-0155. Their financial support is gratefully acknowledged.     

具有熵约束的多阶段均值—半绝对偏差投资组合优化

考虑投资者面临金融市场随机不确定性,将证券收益率视为随机变量,文章运用半绝对偏差度量风险,采用投资组合的熵度量分散化程度,同时,考虑交易成本和借款限制,提出多阶段投资组合模型。由于投资过程存在交易成本,上述模型为路径依赖性的动态优化问题。文章运用离散近似迭代法求解,并证明了该算法是线性收敛的。最后,通过实证研究得出熵的取值越大,投资组合的最终财富越小。