线性无量纲化方法的性质分析

内容提要：在对多种线性无量纲化方法特点分析的基础上,给出了“理想无量纲化方法”应该满足的一些性质,并证明了“理想无量纲化方法不存在”的结论。提出了“构建逼近理想性质的复合无量纲化方法”的思路,并构造了一种优良的复合无量纲化方法——“极标复合法”。提出了指标无量纲化过程的稳定性问题,着重分析造成结果不稳定的“指标数据分布”方面的原因,并给出了一种针对线性无量纲化方法的改进型。     

广义灰色面积关联评价模型及其在科技创新能力评价中的应用

无量纲化处理使得灰色关联评价模型中不同指标之间的计算与比较成为了可能,但同时也破坏了指标数据本身所蕴含的物理属性、数据特征与信息内涵。以时序数据之间的面积相关关系为基础,提出一种广义灰色面积关联评价模型,即计算同类指标的面积相关性,根据指标权重对各方案进行综合加权,并对评估方案进行排序比较;该模型规避了无量纲化处理可能导致的评价结果与实际情况相悖的现象,应用该模型评价长江经济带各省市科技创新能力,结果显示其评价结果的合理性优于经典的邓氏关联评价模型。     

综合评价方法中的最优无量纲化模型研究

针对综合评价过程中无量纲化方法选择盲目性较强的问题,文章首先引入综合评价结果优良性的度量指标,优化综合评价结果稳定性和区分度的度量函数,建立无量纲化有效性的统计检验方法;其次,以无量纲化有效为主要约束条件,分别以稳定性最高、区分度最高以及稳定性和区分度均最高为目标函数构建三类最优无量纲化模型,分析大平移尺度和小平移尺度约束条件对最优无量纲化模型的影响;最后,通过大量的数值模拟实验研究了6种常用综合评价方法中的最优无量纲化模型,并对结果进行深入分析。研究发现,大平移尺度约束下几种综合评价方法中的最优无量纲化结果均不同于现有无量纲化方法,小平移尺度约束下的最优无量纲化与均值化较为接近,但不完全相同;经过不断优化后的稳定性函数和区分度函数能更科学地度量综合评价结果的稳定性和区分度大小,无量纲化有效性的统计检验方法能准确判断指标间的量纲差异是否被有效消除;综合评价方法、目标函数和约束条件不同时所对应的最优无量纲化结果不同。     

线性综合评价模型中指标标准化方法的比较与选择

分析与比较各种指标一致化与无量纲化方法对综合评价结果的影响,并构建兼容度指标对无量纲化方法的相对有效性进行测度。结果表明：在线性综合评价模型中,减法一致化方法、Z-Score法和极差化法相比其他标准化方法更为有效。选择合适的指标标准化方法,能够有效提高综合评价结果的准确性。     

指标无量纲化方法对综合评价结果可靠性的影响及其实证分析

文章认为无量纲化方法的合理性取决于运用该方法对被评对象进行等级排序的合理性。根据序号总和理论,在逐步探寻合理等级排序依据的前提下,可以根据各无量纲化方法所做的等级排序与合理等级排序的等级相关系数来进行无量纲化方法的优选,并通过实证分析得出了相应的结论。     

本期导读

长期以来,学者们对综合评价方法、指标选择和权重设置的研究十分广泛且深入,但对指标无量纲化方面的研究较为薄弱。《大样本评价的定量指标无量纲化方法》一文作者,针对大样本评价的特点,提出了一种结合指标原始数据的客观特性与专家主观经验的定量指标无量纲化方法,分别就大样本评价中的正指标、负指标、中间型指标及复合型指标等定量指标给出了相应情形下的指标归一化计算模型。该方法对大样本评价的定量指标处理具有指标评分分布合理、评价结果区分度高、可操作性强的优点。     

居民物价压力计量理论、模型及实证

不断上涨的物价水平对居民的日常生活产生了很大的压力,准确测度不同收入阶层居民的物价压力情况是目前学术界急需研究的问题。根据物理学压强理论的启示,运用综合指标法与线性无量纲化技术,提出了居民物价压力计量理论,构建物价压力计量模型,并且对不同收入阶层居民的物价动态压力进行计量。实证分析发现:居民的物价动态压力取决于CPI与居民收入两个变量的相对变化方向与幅度,不同收入之间、城乡之间、不同地域之间居民的物价动态压力是有差异的;西方部分发达国家居民的物价动态压力大于国内居民的物价动态压力。     

评价指标的非线性无量纲模糊处理方法

文章阐述了评价指标无量纲处理在综合评价中的重要作用，针对目前评价实践中存在的问题，运用指数函数和模糊数学的有关知识和方法，提出了适用于现行多数评价指标的一种非线性无量纲模糊处理方法。文中介绍了处理模型应具备的性质，分别就正指标、逆指标和适度指标给出了其相应的非线性模糊量化模型及模型中标准值的确定方法     

对《统计评价学》框架体系建设的思考

在进行综合评价的过程中,主要是利用统计特有的手段、方法和统计资料来进行,因而综合评价又称之为统计评价。分别从国民经济和社会发展的现实实践和统计学科建设的角度论证了建立《统计评价学》的必要性,从综合评价的基本理论、评价指标体系的建立、指标权数的确定、无量纲化处理、综合评价的模型方法及综合评价结果的统计分析方法等方面提出了《统计评价学》基本框架体系。     

综合评价指标筛选及预处理的方法研究

本文对综合评价指标筛选及预处理的方法研究,得出多指标综合评价时,首先要对指标进行预处理,包括:必须在多个信息的重迭指标中筛选有效评价指标;必须将指标一致化;要将无量纲化处理。每一个步骤都有多种方法,应用时,应根据实际情况选择合适的方法。     

A comparison of various methods for estimating the parameters in mixtures of von mises distributions

In this paper we compare five methods for estimating the unknown parameters in a mixture of two von Mises distributions. We propose a new method based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have been successfully applied only to linear data. Here we show that the application to circular data is reasonably straightforward and that convergence to the final estimates is fairly rapid. For various simulated known mixtures the results obtained are satisfactory. Finally, we introduce a modification of the method of moments which is considerably faster in CPU time than any of the other methods used and gives good results.     

On the linear degradation model with multiple failure modes

The purpose of this work is to develop statistical methods for using degradation measure to estimate a survival function for a linear degradation model. In this paper, we review existing methods and then describe a parametric approach. We focus on estimating the survival function. A simulation study is conducted to evaluate the performance of the estimating method and the method is illustrated using real data.     

Parametric Estimator of Linear Model with Interval-Censored Data

In this article, we consider the estimation of regression parameters in linear model in the presence of interval-censored data. When the response variable is interval-censored, the traditional methods can not be used to estimate the parameters directly. In this article, unbiased transformation is carried out and a new random variable which has the same expectation as the function of the response variable is established. With the regression analysis for the constructed statistic we conclude the estimator by least square method.     

An alternative circular smoothing method to nonparametric estimation of periodic functions

This article provides alternative circular smoothing methods in nonparametric estimation of periodic functions. By treating the data as ‘circular’, we solve the “boundary issue” in the nonparametric estimation treating the data as ‘linear’. By redefining the distance metric and signed distance, we modify many estimators used in the situations involving periodic patterns. In the perspective of ‘nonparametric estimation of periodic functions’, we present the examples in nonparametric estimation of (1) a periodic function, (2) multiple periodic functions, (3) an evolving function, (4) a periodically varying-coefficient model and (5) a generalized linear model with periodically varying coefficient. In the perspective of ‘circular statistics’, we provide alternative approaches to calculate the weighted average and evaluate the ‘linear/circular–linear/circular’ association and regression. Simulation studies and an empirical study of electricity price index have been conducted to illustrate and compare our methods with other methods in the literature.     

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.     

A Unified Method for Checking Compatibility and Uniqueness for Finite Discrete Conditional Distributions

Checking compatibility for two given conditional distributions and identifying the corresponding unique compatible marginal distributions are important problems in mathematical statistics, especially in Bayesian inferences. In this article, we develop a unified method to check the compatibility and uniqueness for two finite discrete conditional distributions. By formulating the compatibility problem into a system of linear equations subject to constraints, it can be reduced to a quadratic optimization problem with box constraints. We also extend the proposed method from two-dimensional cases to higher-dimensional cases. Finally, we show that our method can be easily applied to checking compatibility and uniqueness for a regression function and a conditional distribution. Several numerical examples are used to illustrate the proposed method. Some comparisons with existing methods are also presented.     

Nonparametric estimation of the link function including variable selection

Nonparametric methods for the estimation of the link function in generalized linear models are able to avoid bias in the regression parameters. But for the estimation of the link typically the full model, which includes all predictors, has been used. When the number of predictors is large these methods fail since the full model cannot be estimated. In the present article a boosting type method is proposed that simultaneously selects predictors and estimates the link function. The method performs quite well in simulations and real data examples.     

Ridge estimation in generalized linear models and proportional hazards regressions

Conventionally, a ridge parameter is estimated as a function of regression parameters based on ordinary least squares. In this article, we proposed an iterative procedure instead of the one-step or conventional ridge method. Additionally, we construct an indicator that measures the potential degree of improvement in mean squared error when ridge estimates are employed. Simulations show that our methods are appropriate for a wide class of non linear models including generalized linear models and proportional hazards (PHs) regressions. The method is applied to a PH regression with highly collinear covariates in a cancer recurrence study.