Adaptive normal reference bandwidth based on quantile for kernel density estimation

Bandwidth selection is an important problem of kernel density estimation. Traditional simple and quick bandwidth selectors usually oversmooth the density estimate. Existing sophisticated selectors usually have computational difficulties and occasionally do not exist. Besides, they may not be robust against outliers in the sample data, and some are highly variable, tending to undersmooth the density. In this paper, a highly robust simple and quick bandwidth selector is proposed, which adapts to different types of densities.     

Estimation using plug-in of the stationary distribution and Shannon entropy of continuous time Markov processes

A natural way to deal with the uncertainty of an ergodic finite state space Markov process is to investigate the entropy of its stationary distribution. When the process is observed, it becomes necessary to estimate this entropy.We estimate both the stationary distribution and its entropy by plug-in of the estimators of the infinitesimal generator. Three situations of observation are discussed: one long trajectory is observed, several independent short trajectories are observed, or the process is observed at discrete times. The good asymptotic behavior of the plug-in estimators is established. We also illustrate the behavior of the estimators through simulation.     

基于购买行为RFM及评论行为RFMP模型的客户终身价值研究

在Web2.0时代,越来越多的消费者在购物网站、点评类网站以及社交类网站上发表自己对产品或服务的相关看法,由此对企业产生了巨大的影响。针对用户在线评论行为所产生的价值,以传统的RFM模型为基础构建了基于评论行为的RFMP模型。同时将购买RFM和评论RFMP模型进行结合,提出了适用于线上企业的客户终身价值评价方法,采用熵值法进行了指标权重的确定,并最终选取大众点评网的实际用户数据进行了传统客户终身价值与改进客户终身价值的对比。通过对用户群进行细分,为企业提供了更加精准的营销决策及管理建议。     

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).     

Nonparametric Kernel Methods with Errors‐in‐Variables: Constructing Estimators,Computing them,and Avoiding Common Mistakes

Estimating a curve nonparametrically from data measured with error is a difficult problem that has been studied by many authors. Constructing a consistent estimator in this context can sometimes be quite challenging, and in this paper we review some of the tools that have been developed in the literature for kernel‐based approaches, founded on the Fourier transform and a more general unbiased score technique. We use those tools to rederive some of the existing nonparametric density and regression estimators for data contaminated by classical or Berkson errors, and discuss how to compute these estimators in practice. We also review some mistakes made by those working in the area, and highlight a number of problems with an existing R package decon .     

长株潭城市群主体功能区划分研究

在《全国主体功能区规划》对长株潭城市群"重点开发区"功能定位的框架下,从资源环境承载力、现有开发密度和发展潜力三方面选取18个指标,构建长株潭城市群主体功能区划分指标体系,运用熵权法、多目标线性加权函数法等数理方法,结合当地实际,将长株潭城市群划分为优化开发区、重点开发区、一般开发区、限制开发区、禁止开发区五类主体功能区,并提出各功能区的发展方向与建设策略。     

基于融合熵特征的辐射源信号识别

针对相近雷达辐射源信号难以识别的问题,一种新的雷达辐射源信号识别方法被提出.该方法基于小波包分解,用主成分分析法融合含有信号类别特性的小波包重构系数特征,并将融合特征的能量熵和概率熵构成特征向量,基于支持向量机实现信号的分类识别.在较大信噪比(SNR)范围内,使用该方法能获得满意的正确识别率,当SNR为5 dB时,十分近似的线性调频信号正确识别率达到了91%,实验结果证实了该方法的有效性.     

基于谱熵法的火箭弹开舱点测量研究

提出了一种基于谱熵的火箭弹开舱点测量方法,当火箭弹开舱时,雷达反射截面积(RCS)、多普勒频率突变引起谱熵突变,从而检测开舱点.该方法充分利用了RCS、多普勒突变信息,避免了单独利用RCS、多普勒突变信息带来的局限,解决了相参积累时间短,频域分不开时的开舱点检测问题.实验结果表明,该方法能较精确地测量开舱点.     

建筑企业承包商选择的综合评价方法研究

传统的建筑行业选择承包商时主观的成分过多,且多集中在承包商的价格、资质等方面,尚未形成全面的评价指标体系。针对承包商选择中存在的不足,从复杂系统的角度出发,构建了建筑企业承包商选择的综合评价指标体系。该体系包含了承包商的社会影响力、技术能力、工程管理能力、市场开拓与营销能力、融资与财务能力和资源管理能力等指标,使评价体系更合理全面。同时采用熵权法确定指标的权重,尽量消除人为因素干扰。