多指标综合评价中的逆序问题研究

一、逆序问题的提出 多指标综合评价一般由三大基本要素构成：评价对象集、评价目标（标准）、评价方法。评价对象集往往由若干个被评价的单位或元素构成，它们可以是不同时间如年份（这种评价称为动态评价或纵向评价），也可以是不同空间如地区或国家、部门、基层单位等（这种评价称为静态评价或横向评价）。评价目标则是判断评价对象价值水平之高低或质量状态之优劣的一种标准，它往往受评价方法甚至评价对象集的影响。评价方法则是对评价对象集元素进行量化评价的模型，包括评价指标体系、构权方法、权值体系、同度量化（或称无量纲化）…     

外汇储备最优规模测度模型的比较研究

文章分析了国外有代表性的外汇储备最优规模的测度模型,并对各种模型进行比较和评价,在此基础上得出了几点启示性的结论：（1）外汇储备最优规模的度量模型随着外汇储备功能的演变而发展;（2）各种度量模型是一种相对独立,相互影响及相互补充的关系;（3）外汇储备最优规模的度量模型是动态的;（4）没有通用的度量最优外汇储备规模的模型。     

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。     

地区间经济发展水平综合评价比较方法

一、综合评价的意义 所谓综合评价是我们将不同的统计指标转化为同度量因素,综合为一个具有可比性的指标,并进行的评价。综合评价的结果用于研究和分析     

论综合指数和平均数指数

综合指数和平均数指数在由简单形式发展到加权形式的过程中,源于L氏指数和P氏指数中同度量因素（权数）的选择和时间的固定的不同,在其编制和计算中形成了L氏指数法和P氏指数法—由此,加权综合指数和加权平均数指数构成了当代编制与计算总指数中最重要最基本的两种形式。于是在编制质量指标指数和数量指标指数时,分别采用P氏指数法和L氏指数法。加权综合指数和加权平均数指数在二者的变量（或指数化因素或指数化指标）和同度量因素（权数）、分子分母资料的表现形式、对资料的要求和使用等三方面有不同之处,但后者是前者的变形。     

运用多元统计进行综合评价的一个思路

综合评价是统计方法体系中的一个重要分支，对于数值型多指标综合评价问题，如果各指标之间存在较高的相关性，采用多元统计方法进行综合评价可以取得较为良好的评价效果。但是研究表明，传统的主成分分析和因子分析两种方法单独运用于综合评价存在一定的问题，本文分析了两种方法在综合评价中的适用性，梳理出一个结合运用两种方法进行综合评价的思路（FA—PCA综合评价模型）。     

确定指标权重的统计方法比较

一、引言指标权重是各个指标因素在评价过程中重要程度的反映,是指标相对重要性的一种综合度量。指标权重确定的合理与否,直接关系到整个评价体系的科学性。评价指标存在于单目标或多目标决策体系当中,是决策的一个重要环节,对于处在不同评价体系中的指标,     

基于复杂性的供应链复合评价方法

对基于复杂性的供应链的协同评价不仅要考虑经济指标,而且要将供应链的不确定性、可靠性,以及其经济效益和发展潜能进行综合评价.这种协同评价既包含随机性和概率约束,又有时序性要求.这就面临将不确定的度量指标——熵与可靠性指标——可靠度,以及经济指标和发展潜能指标进行复合评价的问题,需要建立适应和满足这种复合评价的教学模型.文章对具有时序性要求的确定性DEA模型进行了改进,引入了熵和可靠度指标,综合集成出熵——随机DEA的供应链协同评价模型.     

浅议TOPSIS在企业信用综合评价中的应用

现行或潜在的债权人、投资者客观准确地对企业信用进行综合评价，然后据以科学计划与决策，是降低风险、增加收益的一个必不可少的环节。然而对企业信用进行综合评价涉及到的指标很多，且每个指标在各个企业间表现差别很大，各个指标又不能用统一标准度量。因此，除了建立科学、合理的评价指标体系外，还要借助于科学的评价方法。本文试将多目标决策分析中的TOPSIS方法用于企业信用综合评价。一、TOPSIS评价方法基本原理TOPSIS是多目标决策分析中的一类决策方法：即逼近理想解的“排序方法（TechniqueforOrderPreferencebySimilari…     

论两种综合评价国民经济整体效益方法的问题

目前用于评价国民经济效益的主要方法有综合指数法和功效系数法。这两种方法将国民经济效益指标体系中各项不同性质的指标转化为同度量的指标,解决了多指标的综合问题。但这两种方法存在着重大缺陷。一、同时运用综合指数法和功效系数法时,其评价结论有时是不一致的一个...     

Robustness of designed experiments against missing data

This paper investigates the robustness of designed experiments for estimating linear functions of a subset of parameters in a general linear model against the loss of any t( ≥1) observations. Necessary and sufficient conditions for robustness of a design under a homoscedastic model are derived. It is shown that a design robust under a homoscedastic model is also robust under a general heteroscedastic model with correlated observations. As a particular case, necessary and sufficient conditions are obtained for the robustness of block designs against the loss of data. Simple sufficient conditions are also provided for the binary block designs to be robust against the loss of data. Some classes of designs, robust up to three missing observations, are identified. A-efficiency of the residual design is evaluated for certain block designs for several patterns of two missing observations. The efficiency of the residual design has also been worked out when all the observations in any two blocks, not necessarily disjoint, are lost. The lower bound to A-efficiency has also been obtained for the loss of t observations. Finally, a general expression is obtained for the efficiency of the residual design when all the observations of m ( ≥1) disjoint blocks are lost.     

Efficient estimation of general linear mixed effects models

An extension of the linear growth curve model (Biometrics 38 (1982) 963) was proposed by Stukel and Demidenko (Biometrics 53 (1997) 720) to study the effects of population covariates on one or more characteristics of the curve, when the characteristics are expressed as linear combinations of the growth curve parameters. In the present paper, this general growth curve model receives a comprehensive theoretical treatment. A two-stage estimator, consisting of a generalized least squares estimator under constraints for the population parameters and a moment estimator for the variance parameters, is developed for application in the non-Gaussian error situation. Two likelihood based estimators, global maximum likelihood and second-stage maximum likelihood, are also developed. It is shown that all three estimators are consistent, asymptotically normally distributed, and efficient, and are equivalent when the number of individuals tends to infinity. An expression for the bias in the estimator of the population parameters is derived under second stage model misspecification. We show that if parameters that are not of primary interest are incorrectly specified, bias may occur in parameters that are of interest using the standard growth curve model. The general growth curve model does not require specification of such nuisance parameters and is robust in terms of bias. The general linear growth curve model is used to study the effects of host sex on pancreatic tumor growth in rats.     

Robustness of bayesian factor analysis estimates

This paper presents the result of a study of the robustness of posterior estimators of the factor loading matrix, the factor scores, and the disturbance covariance matrix (the main model parameters) in a Bayesian factor analysis with respect to variations in the values of the parameters of their prior distributions (the hyperparameter). We adopt the ε - contamination model of Berger and Berliner(1986) to generate prior distributions whose hyper-paramters reflects small variations in the elements of the uncontaminated hyperparameters, and we use directional derivatives to examine the variation of the uncontaminated estimators with respect to changes in the values of the hyperparameters, in the directions of the main model parameters. Several matrix norms are used to measure the closeness of the resulting values. We illustrate the results with a numerical example.     

A sequential method for the evaluation of the VaR model based on the run between exceedances

Summary: A technique for sequential assessment of the appropriateness of the VaR model is developed, by drawing on a tool from statistical process control, namely the control chart. We show that an EWMA control chart is the most appropriate instrument for detecting changes in the process of the magnitude of interest in risk management. The robustness of our procedure with respect to violations of some assumptions is examined and it is concluded that our model evaluation technique remains suitable in such cases.     

Robustness and maximum likelihood estimation

The usual concept of robustness is called "criterion" or "non-adaptive" robustness to distinguish it from "inference" or "adaptive" robustness. The former term is appled to describe relative insensitivity to changes in the parent distribution, while the latter specifically implies dependence on and hence adaptation to changes in the parent distribution. It is argued that knowledge of, and sensitivity to the parent distribution is an important aspect of inference, and thus the latter concept of robustness is more relevant than the former. This focuses attention on adaptive procedures that use most of the sample information, that is, are efficient. Maximum likelihood has been criticized as depending critically on knowledge of the exact parent distribution, and hence of lacking criterion or non-adaptive robustness. This might have been justified when computational parameter to allow for uncertainly of shape. then the method of maximim likelihood is hsown to possess the more important requirement of being adaptive and efficent, capable of assessing the more relevant creiterion of inference or adaptive robustness.     

Robust estimation of a multilevel model with structural change

We postulate a spatiotemporal multilevel model and estimate using forward search algorithm and MLE imbedded into the backfitting algorithm. Forward search algorithm ensures robustness of the estimates by filtering the effect of temporary structural changes in the estimation of the group-level covariates, the individual-level covariates and spatial parameters. Backfitting algorithm provides computational efficiency of estimation procedure assuming an additive model. Simulation studies show that estimates are robust even in the presence of structural changes induced for example by epidemic outbreak. The model also produced robust estimates even for small sample and short time series common in epidemiological settings.     

An evaluation of the Bayesian approach to fitting the N-mixture model for use with pseudo-replicated count data

The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.     

Asymptotic study of the change-point mle in multivariate Gaussian families under contiguous alternatives

The problem of estimating an unknown change-point in the mean vector or covariance matrix of a sequence of independent multivariate Gaussian random variables is considered. Adapting the estimation methodology that Hinkley pursued for the case of abrupt changes, we develop theory for deriving the asymptotic distribution of the maximum likelihood estimator of the change-point when the amount of change is a function of the sample size and goes to zero in a smooth fashion as the sample size goes to infinity, yielding a contiguous change-point model. Simulations have been performed to illustrate the closeness of the asymptotic distribution with the empirical distribution, and to evaluate its robustness to departures from normality for reasonable sample sizes as well as parameter changes. Finally, we apply the methodology to estimate the change-point in the daily log-returns data of BLS (BellSouth) and VZ (Verizon) from NYSE.     

Some recent advances in measurement error models and methods

Summary A measurement error model is a regression model with (substantial) measurement errors in the variables. Disregarding these measurement errors in estimating the regression parameters results in asymptotically biased estimators. Several methods have been proposed to eliminate, or at least to reduce, this bias, and the relative efficiency and robustness of these methods have been compared. The paper gives an account of these endeavors. In another context, when data are of a categorical nature, classification errors play a similar role as measurement errors in continuous data. The paper also reviews some recent advances in this field. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the frame of the Sonderforschungsbereich SFB 386. We thank two anonymous referees for their helpful comments.     

Analysis of rounded data in measurement error regression

The measurement error model (MEM) is an important model in statistics because in a regression problem, the measurement error of the explanatory variable will seriously affect the statistical inferences if measurement errors are ignored. In this paper, we revisit the MEM when both the response and explanatory variables are further involved with rounding errors. Additionally, the use of a normal mixture distribution to increase the robustness of model misspecification for the distribution of the explanatory variables in measurement error regression is in line with recent developments. This paper proposes a new method for estimating the model parameters. It can be proved that the estimates obtained by the new method possess the properties of consistency and asymptotic normality.