灰色聚类评价方法的延拓研究

本文对传统灰色聚类方法进行了延拓,考察了其白化权函数转折点选择问题。首先,阐述灰色聚类评价中白化权函数的确定方法,并指出其弊端;然后,提出基于区间灰数的白化权函数转折点确定方法,给出灰色聚类评价方法的延拓方案;最后,应用实例验证方法的有效性。     

基于灰色判断矩阵的一致性及其排序研究

对灰色层次分析法中基于灰色判断矩阵的一致性和排序问题进行了研究。提出了灰色判断矩阵的弱一致性和乘性完全一致性的条件,然后讨论了在单一准则下基于灰色判断矩阵的方案集排序问题。方法一将灰色判断矩阵转化为白化矩阵,通过研究白化矩阵的性质来对方案集进行排序,方法二是将其转化为区间灰数互补判断矩阵,再利用OWA算子对方案集集结进而进行排序。最后通过算例说明了该方法的有效性。     

灰色聚类法在课程评估中的应用

灰色聚类是以灰数的白化函数生成为基础的一种聚类方法。文章首先提出采用加权平均法则，对聚类结果可进行再分析，以充分利用信息，使评判结果更为合理。同时应用灰色聚类法对西安统计学院４门课程进行了综合评价分析，其结果符合实际。     

旅游产业发展的冲击认知分析

文章将提出一种Pareto改进型的灰色评估方法并对旅游产业发展的冲击进行综合评价。对已有的端点型三角白化权函数进行帕累托改进,构建了一类基于双重灰类隶属点垂直滑脱的Pareto改进型白化权函数。针对灰色评估的聚类特性,提出三条帕累托改进有效性准则:区分度增强准则、规范性准则以及隶属度清晰准则,进而对改进之后的白化权函数进行有效性分析,结果表明改进之后的白化权函数表现出了很好的灰色评估聚类特性。文章提出的改进后的白化权函数以及帕累托改进有效性准则能够为灰色评估方法的发展演进提供有益的方向性指导。     

灰色聚类方法在高校图书馆综合评估中的应用

文章根据高校图书馆综合评估的要求和统计数据特点,应用灰色聚类方法进行多指标数据的权重计算和白化处理,结合SPSS和Metlab软件应用,实现了多评价指标的科学赋权和图书馆的分类排名,是对高校图书馆综合评估计算方法的有益探讨。     

基于多专家灰色综合评价的企业财务危机预警方法

针对财务危机定量预警方法忽视专家的经验知识以及非财务信息的局限性,文章提出基于灰色综合评价的多专家群决策财务危机预警方法。首先,设计了包含两个层次的财务危机预警定性指标体系及其评分标准。然后,根据财务危机预警的特点,构建了财务危机可能性的灰色综合评价模型,具体设置了企业财务危机可能性评价的灰类及其对应的灰数和白化权函数。最后,通过算例说明基于灰色综合评价进行企业财务危机群决策预警的具体过程。     

基于多专家灰色综台评价的企业财务危机预警方法

针时财务危机定量预警方法忽视专家的经验知识以及非财务信息的局限性,文章提出基于灰色综合评价的多专家群决策财务危机预警方法.首先,设计了包含两个层次的财务危机预警定性指标体系及其评分标准.然后,根据财务危机预警的特点,构建了财务危机可能性的灰色综合评价模型,具体设置了企业财务危机可能性评价的灰类及其对应的灰数和白化权函数.最后,通过算例说明基于灰色综合评价进行企业财务危机群决策预警的具体过程.     

灰色系统综合评价在人力资源估价中的应用

人力资源的价值由于受非货币因素影响较多,难以精确地计量出一个数据作为价值尺度。本文采用灰色系统综合评价方法,将评价法的分散信息由白化权函数处理成一个描述不同灰类程度的权向量,在此基础上,再对其进行单值化处理,便可得到受评者的综合评价值,具有良好的应用前景。     

基于白化权函数分类区分度的变权灰色聚类

针对灰色聚类指标权重确定的问题,通过定义白化权函数的分类区分度来度量各指标对聚类对象的分类所作的贡献,并据此确定分类指标的权重。在此基础上,提出了变权灰色聚类方法。结果表明,该方法能够融合聚类对象的样本信息和专家的经验,有效确定不同聚类对象的各指标权重,且适用于聚类指标的量纲不同、数量级悬殊较大的情形。最后通过一个实例说明了变权灰色聚类的实用性和有效性。     

基于区间数观察值的灰色白化权函数聚类模型重构

针对区间数观察值的白化权函数取值范围是一个区间数的思路,文章结合单一实数值不同测度白化权在不同区段内白化权取值的增减特性,给出一种基于区间数观察值的典型、上限、三角、下限测度白化权函数的新算法,并结合区间数可能度排序方法,提出了新的对于区间数观察值的灰色白化权函数聚类决策步骤.并验证了本文算法的有效性.     

无偏灰色Verhulst直接建模模型及其优化

针对本身已经具有饱和状态过程且近似满足Logistic函数形式的原始序列,提出通过对其进行倒数生成,建立无偏灰色Verhulst直接建模模型,并在此基础上将同时优化背景值和灰导数与利用"最小一乘法"确定响应系数的方法相结合,从而建立了优化的无偏灰色Verhulst直接建模模型。结果表明,该模型对满足Logistic函数形式的曲线进行模拟和预测具有完全重合性。通过实例分析说明了优化的新模型的可行性和有效性。     

一种适用于非齐次指数增长序列的直接型离散灰色模型

基于灰色模型的背景值表达式及非齐次指数增长序列的形式1,得到了一种一次累加序列与原始序列的关系,给出了系数确定方法,获得了适用于非齐次指数增长序列的直接型离散灰色模型,并给出了系数确定的方法。实例研究表明：本优化模型不仅具有可操作性,而且精度高,效果好。     

Semi-supervised Bayesian adaptive multiresolution shrinkage for wavelet-based denoising

We can use wavelet shrinkage to estimate a possibly multivariate regression function g under the general regression setup, y = g + ε. We propose an enhanced wavelet-based denoising methodology based on Bayesian adaptive multiresolution shrinkage, an effective Bayesian shrinkage rule in addition to the semi-supervised learning mechanism. The Bayesian shrinkage rule is advanced by utilizing the semi-supervised learning method in which the neighboring structure of a wavelet coefficient is adopted and an appropriate decision function is derived. According to decision function, wavelet coefficients follow one of two prespecified Bayesian rules obtained using varying related parameters. The decision of a wavelet coefficient depends not only on its magnitude, but also on the neighboring structure on which the coefficient is located. We discuss the theoretical properties of the suggested method and provide recommended parameter settings. We show that the proposed method is often superior to several existing wavelet denoising methods through extensive experimentation.     

Boundary detection through dynamic polygons

A method for the Bayesian restoration of noisy binary images portraying an object with constant grey level on a background is presented. The restoration, performed by fitting a polygon with any number of sides to the object's outline, is driven by a new probabilistic model for the generation of polygons in a compact subset of R² , which is used as a prior distribution for the polygon. Some measurability issues raised by the correct specification of the model are addressed. The simulation from the prior and the calculation of the a posteriori mean of grey levels are carried out through reversible jump Markov chain Monte Carlo computation, whose implementation and convergence properties are also discussed. One example of restoration of a synthetic image is presented and compared with existing pixel-based methods.     

Optimal estimation in functional linear regression for sparse noise‐contaminated data

In this article, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions. We consider the case where the response and the predictor processes are both sparsely sampled at random time points and are contaminated with random errors. In addition, the random times are allowed to be different for the measurements of the predictor and the response functions. The aforementioned situation often occurs in longitudinal data settings. To estimate the covariance and the cross‐covariance functions, we use a regularization method over a reproducing kernel Hilbert space. The estimate of the cross‐covariance function is used to obtain estimates of the regression coefficient function and of the functional singular components. We derive the convergence rates of the proposed cross‐covariance, the regression coefficient, and the singular component function estimators. Furthermore, we show that, under some regularity conditions, the estimator of the coefficient function has a minimax optimal rate. We conduct a simulation study and demonstrate merits of the proposed method by comparing it to some other existing methods in the literature. We illustrate the method by an example of an application to a real‐world air quality dataset. The Canadian Journal of Statistics 47: 524–559; 2019 © 2019 Statistical Society of Canada     

B-spline estimation for partially linear varying coefficient composite quantile regression models

Abstract

In this article, a new composite quantile regression estimation (CQR) approach is proposed for partially linear varying coefficient models (PLVCM) under composite quantile loss function with B-spline approximations. The major advantage of the proposed procedures over the existing ones is easy to implement using existing software, and it requires no specification of the error distributions. Under the regularity conditions, the consistency and asymptotic normality of the estimators are also derived. Finally, a simulation study and a real data application are undertaken to assess the finite sample performance of the proposed estimation procedure.     

Semivarying coefficient least-squares support vector regression for analyzing high-dimensional gene-environmental data

In the context of genetics and genomic medicine, gene-environment (G×E) interactions have a great impact on the risk of human diseases. Some existing methods for identifying G×E interactions are considered to be limited, since they analyze one or a few number of G factors at a time, assume linear effects of E factors, and use inefficient selection methods. In this paper, we propose a new method to identify significant main effects and G×E interactions. This is based on a semivarying coefficient least-squares support vector regression (LS-SVR) technique, which is devised by utilizing flexible semiparametric LS-SVR approach for censored survival data. This semivarying coefficient model is used to deal with the nonlinear effects of E factors. We also derive a generalized cross validation (GCV) function for determining the optimal values of hyperparameters of the proposed method. This GCV function is also used to identify significant main effects and G×E interactions. The proposed method is evaluated through numerical studies.     

Outlier detection using difference-based variance estimators in multiple regression

In this article, we propose an outlier detection approach in a multiple regression model using the properties of a difference-based variance estimator. This type of a difference-based variance estimator was originally used to estimate error variance in a non parametric regression model without estimating a non parametric function. This article first employed a difference-based error variance estimator to study the outlier detection problem in a multiple regression model. Our approach uses the leave-one-out type method based on difference-based error variance. The existing outlier detection approaches using the leave-one-out approach are highly affected by other outliers, while ours is not because our approach does not use the regression coefficient estimator. We compared our approach with several existing methods using a simulation study, suggesting the outperformance of our approach. The advantages of our approach are demonstrated using a real data application. Our approach can be extended to the non parametric regression model for outlier detection.     

New Ridge Regression Estimator in Semiparametric Regression Models

In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Many efforts have been put to develop the computation of risk function in different full-parametric ridge regression approaches using eigenvalues and then bringing an efficient estimator of shrinkage parameter based on them. In this respect, the estimation of shrinkage parameter is neglected for semiparametric regression model. Not restricted, but the main focus of this approach is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression. For this purpose the differencing methodology is applied. We also propose a new estimator for shrinkage parameter which is of harmonic type mean of ridge estimators. It is shown that this estimator performs better than all the existing ones for the regression coefficient. For our proposal, a Monte Carlo simulation study and a real dataset analysis related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on the minimum risk and mean squared error criteria.     

关于组合评价法的事前事后检验

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