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。     

GRA方法中的无量纲化比较

由于人们对事物的认识具有广泛的灰色性,即信息的不完全性和不确定性,灰色理论由此产生,并得到广泛的应用,但在关联度分析中,无量纲的处理不同得出的结论有时是矛盾的,本文旨在阐述这一问题.     

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。     

熵值法中无量纲化方法优良标准的探讨

在综合评价中,基于"差异驱动"原理的熵值法得到了广泛的应用,随之而来的是应用各种无量纲化方法对其进行改进。由于无量纲化方法有其各自的特点和适用范围,因此其各自的改进熵值法不可避免地存在优良性差异。文章通过理论推导与实证分析,对各改进熵值法的优良性进行探讨,最终得到最优的方法——极值熵值法,即极值处理法和熵值法的结合。     

关于多指标综合评价中指标正向化和无量纲化方法的选择

在多指标综合评价中,有些是指标值越大评价越好的指标,称为正向指标(也称效益型指标或望大型指标);有些是指标值越小评价越好的指标,称为逆向指标(也称成本型指标或望小型指标),还有些是指标值越接近某个值越好的指标,称为适度指标。在综合评价时,首先必须将指标同趋势化,一般是将逆向指标和适度指标转化为正向指标,所以也称为指标的正向化。不同评价指标往往具有不同的量纲和量纲单位,为了消除由此带来的不可公度性,还应将各评价指标作无量纲化处理。指标的同趋势化和无量纲化都有多种方法,应用时,应根据实际情况选择合适的方法。否则将会…     

线性无量纲化方法比较研究

根据线性无量纲化方法函数构成所使用的中心点值和值域指标以及其斜率和截距的表达式,对8种线性无量纲化方法进行分析,从不同的角度再次论证不同线性无量纲化方法所满足的性质定理,并进行了理论论证。同时,通过对线性无量纲化方法的分类比较,结合相关性质定理提出了多种线性无量纲化方法,并说明了其相关性质,具有一定的科学性。同时还分析了在对多指标数据进行综合评价的过程中只采用一种线性无量纲化方法的不足,提出了采用多种无量纲化方法的设想的理论可行性,并用案例进行了实证分析,表明其存在一定的合理性。     

无量纲化对属性权重影响的传导机制及调权研究

文章基于离差最大化要求的约束条件与假设冲突以及离差最大化可能造成权重信息失真的问题,以属性下方案的方差为媒介,分析了无量纲化方法对属性权重影响的传导机制,给出了几个重要的结论.同时,依据方差控制要求,给出了权重调整策略,最后通过算例分析对结论进行了检验.     

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     

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。     

函数性广义线性模型曲线选择的正则化方法

本文对函数性广义线性模型曲线选择的正则化方法进行了较全面地综述,并比较了各种方法的性质。结果发现,函数性广义线性模型曲线选择问题具有群组效应,另外可能具有高维数据性质。同时通过数据模拟发现,Group Bridge、Group MCP、Elastic Net和Mnet表现出较好的数值结果。     

A Semiparametric Estimation Approach for Linear Mixed Models

Maximum likelihood approach is the most frequently employed approach for the inference of linear mixed models. However, it relies on the normal distributional assumption of the random effects and the within-subject errors, and it is lack of robustness against outliers. This article proposes a semiparametric estimation approach for linear mixed models. This approach is based on the first two marginal moments of the response variable, and does not require any parametric distributional assumptions of random effects or error terms. The consistency and asymptotically normality of the estimator are derived under fairly general conditions. In addition, we show that the proposed estimator has a bounded influence function and a redescending property so it is robust to outliers. The methodology is illustrated through an application to the famed Framingham cholesterol data. The finite sample behavior and the robustness properties of the proposed estimator are evaluated through extensive simulation studies.     

A note On outlier sensitivity of Sliced Inverse Regression

Sliced Inverse Regression (SIR) is a promising technique for the purpose of dimension reduction. Several properties of this method have been examined already, but little attention has been paid to robustness aspects. In this article, we focus on the sensitivity of SIR to outliers and show in what sense and how severely SIR can be influenced by outliers in the data.     

Multiple Linear Regression Model Under Nonnormality

Abstract

We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.     

George W. Snedecor,Pioneer Statistician, 1881–1974

Users of statistical packages need to be aware of the influence that outlying data points can have on their statistical analyses. Robust procedures provide formal methods to spot these outliers and reduce their influence. Although a few robust procedures are mentioned in this article, one is emphasized; it is motivated by maximum likelihood estimation to make it seem more natural. Use of this procedure in regression problems is considered in some detail, and an approximate error structure is stated for the robust estimates of the regression coefficients. A few examples are given. A suggestion of how these techniques should be implemented in practice is included.     

Weighted likelihood based inference for P(X < Y)

This contribution deals with the statistical problem of evaluating the stress–strength reliability parameter R = P(X < Y), when both stress and strength data are prone to contamination. Standard likelihood inference can be badly affected by mild data inadequacies, that often occur in the form of several outliers. Then, robust tools are recommended. Here, inference relies on the weighted likelihood methodology. This approach has the advantage to lead to robust estimators, tests, and confidence intervals that share the main asymptotic properties of their classical counterparts. The accuracy of the proposed methodology is illustrated both by numerical studies and real-data applications.     

Robust estimation and design procedures for the random effects model

The authors discuss two robust estimators for estimating variance components in the random effects model, and they obtain finite‐sample breakdown points for the estimators. Based on the finite‐sample breakdown point, they propose a criterion for selecting robust designs. With robust designs, one can get efficient and reliable estimates for variance components regardless of outliers which may happen in the experiment. The authors give examples to show the performance of robust estimators and to compare robust designs with optimal designs based on the traditional analysis of variance estimation method.     

A robust approach to joint modeling of mean and scale covariance for longitudinal data

In this paper, we propose a multivariate t$t$ regression model with its mean and scale covariance modeled jointly for the analysis of longitudinal data. A modified Cholesky decomposition is adopted to factorize the dependence structure in terms of unconstrained autoregressive and scale innovation parameters. We present three distinct representations of the log-likelihood function of the model and study the associated properties. A computationally efficient Fisher scoring algorithm is developed for carrying out maximum likelihood estimation. The technique for the prediction of future responses in this context is also investigated. The implementation of the proposed methodology is illustrated through two real-life examples and extensive simulation studies.     

Influential Observations in Time Series

This article studies how to identify influential observations in univariate autoregressive integrated moving average time series models and how to measure their effects on the estimated parameters of the model. The sensitivity of the parameters to the presence of either additive or innovational outliers is analyzed, and influence statistics based on the Mahalanobis distance are presented. The statistic linked to additive outliers is shown to be very useful for indicating the robustness of the fitted model to the given data set. Its application is illustrated using a relevant set of historical data.