客户流失危机分析的决策树方法

叙述了客户流失的基本概念,分析客户流失危机产生的原因,指出了传统的客户流失危机分析方法存在的问题,在ID3算法的基础上,提出一种加权熵的概念,并对ID3算法进行改进,提出了一种基于决策树的客户流失危机分析方法,通过一个客户流失危机的分析实验对该模型进行了验证.实验结果表明该方法是可行的和有效的,为客户流失危机分析和预警提供了一种新的研究思路和分析方法.     

Maximum Entropy Approximations for Asymptotic Distributions of Smooth Functions of Sample Means

Abstract. We propose an information‐theoretic approach to approximate asymptotic distributions of statistics using the maximum entropy (ME) densities. Conventional ME densities are typically defined on a bounded support. For distributions defined on unbounded supports, we use an asymptotically negligible dampening function for the ME approximation such that it is well defined on the real line. We establish order n^?1 asymptotic equivalence between the proposed method and the classical Edgeworth approximation for general statistics that are smooth functions of sample means. Numerical examples are provided to demonstrate the efficacy of the proposed method.     

Rényi entropy properties of records

We provide bounds for Rényi entropy of records. We also show that the Rényi entropy ordering of random variables determines the Rényi entropy ordering of their respective records. We characterize exponential distribution by maximization of Rényi entropy under some conditions. We show that Rényi distance between distribution of records and parent distribution is distribution free.     

基于熵的m维瓶颈指派问题的动态规划解

对m维瓶颈指派问题建立了动态规划模型,并利用熵作为工具给出了动态规划模型的解。最后,通过一个算例说明方法的可行性和有效性。     

Maximum expected entropy transformed Latin hypercube designs

Existing projection designs (e.g. maximum projection designs) attempt to achieve good space-filling properties in all projections. However, when using a Gaussian process (GP), model-based design criteria such as the entropy criterion is more appropriate. We employ the entropy criterion averaged over a set of projections, called expected entropy criterion (EEC), to generate projection designs. We show that maximum EEC designs are invariant to monotonic transformations of the response, i.e. they are optimal for a wide class of stochastic process models. We also demonstrate that transformation of each column of a Latin hypercube design (LHD) based on a monotonic function can substantially improve the EEC. Two types of input transformations are considered: a quantile function of a symmetric Beta distribution chosen to optimize the EEC, and a nonparametric transformation corresponding to the quantile function of a symmetric density chosen to optimize the EEC. Numerical studies show that the proposed transformations of the LHD are efficient and effective for building robust maximum EEC designs. These designs give projections with markedly higher entropies and lower maximum prediction variances (MPV''s) at the cost of small increases in average prediction variances (APV''s) compared to state-of-the-art space-filling designs over wide ranges of covariance parameter values.     

Adaptive Local Polynomial Whittle Estimation of Long‐range Dependence

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short‐run component of the spectrum, ϕ(λ) , by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a “local polynomial Whittle” (LPW) estimator. We specify a data‐dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of ϕ(λ) at zero and selects the bandwidth. The resulting “adaptive LPW” estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of ϕ(λ) at zero, up to a logarithmic factor.     

基于Gini系数和Theil’s标准的陕西省城乡居民收入差距研究

城乡统筹发展是西部大开发的重点问题之一。研究陕西城乡收入差距问题对于制定西部大开发下城乡统筹发展具有借鉴意义。通过利用基尼系数和泰尔熵标准。精确测算了陕西省城乡居民高、中、低层次收入差距,发现改革开放以来陕西省城乡居民收入差距总体上呈上升趋势。到2002年达到阶段性的峰值。弥补了以往定性分析研究的缺陷。并提出解决陕西省城乡统筹发展的对策。     

Deconvolution boundary kernel method in nonparametric density estimation

This paper considers the nonparametric deconvolution problem when the true density function is left (or right) truncated. We propose to remove the boundary effect of the conventional deconvolution density estimator by using a special class of kernels: the deconvolution boundary kernels. Methods for constructing such kernels are provided. The mean squared error properties, including the rates of convergence, are investigated for supersmooth and ordinary smooth errors. Numerical simulations show that the deconvolution boundary kernel estimator successfully removes the boundary effects of the conventional deconvolution density estimator.     

基于竞合模型的广电与互联网联动发展研究

随着信息技术与网络技术的发展和广泛运用,传统广电业与新兴互联网之间的产业边界逐渐变得模糊,融合发展成为新的产业形态,三网融合的推进也使互联网与广电网在产品和服务的提供上越来越趋同,这加剧了广电与互联网之间的竞争,同时也提升了两者的合作空间。在借鉴了互联网视频网站服务评估方法的基础上,从广电产业关心的角度出发,运用层次分析法和熵值法,设计了竞合模式下合作伙伴评估选择的综合评价体系,并依据静态博弈模型构建了双方在具体业务上合作的成本———利润函数模型,为广电企业和互联网企业合作伙伴与合作方式的选择提供理论参考。     

Test for normality based on two new estimators of entropy

In this article, two new consistent estimators are introduced of Shannon's entropy that compares root of mean-square error with other estimators. Then we define new tests for normality based on these new estimators. Finally, by simulation, the powers of the proposed tests are compared under different alternatives with other entropy tests for normality.