Interpoint Distance Classification of High Dimensional Discrete Observations

Classification is a multivariate technique that is concerned with allocating new observations to two or more groups. We use interpoint distances to measure the closeness of the samples and construct new rules for high dimensional classification of discrete observations. Applicable to high dimensional data, the new method is non‐parametric and uses test‐based classification with permutation testing. We propose a modification of a test‐based rule to use relative values with respect to the training samples baseline. We compare the proposed rule with parametric methods, such as likelihood ratio rule and modified linear discriminate function, and non‐parametric techniques such as support vector machine, nearest neighbour and depth‐based classification, under multivariate Bernoulli, multinomial and multivariate Poisson distributions.     

Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model

Assessing regional population compositions is an important task in many research fields. Small area estimation with generalized linear mixed models marks a powerful tool for this purpose. However, the method has limitations in practice. When the data are subject to measurement errors, small area models produce inefficient or biased results since they cannot account for data uncertainty. This is particularly problematic for composition prediction, since generalized linear mixed models often rely on approximate likelihood inference. Obtained predictions are not reliable. We propose a robust multivariate Fay–Herriot model to solve these issues. It combines compositional data analysis with robust optimization theory. The nonlinear estimation of compositions is restated as a linear problem through isometric logratio transformations. Robust model parameter estimation is performed via penalized maximum likelihood. A robust best predictor is derived. Simulations are conducted to demonstrate the effectiveness of the approach. An application to alcohol consumption in Germany is provided.     

上市公司股权结构与股利政策相关性实证分析——西北五省区的数据

本文以2002年~2004年西北五省区有股利分配的上市公司作为样本,采用多元回归分析方法,验证股权结构自变量与股利之间的线性关系,用非线性回归方法检验未通过线性关系检验的自变量与股利之间的关系。结果发现,西北五省区股利偏低,股东对现金股利有不同偏好。     

Multivariate Small Area Estimation of Multidimensional Latent Economic Well-being Indicators

Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well-being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit-level small area estimation approach to predict a vector of means of factor scores representing well-being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data.     

Conditional independence and log linear models for multi-dimensional contingency tables

Interference about conditional independence in relation to log linear models are discussed for contingency tables. The parameters and likelihood ratios for a log linear model with a dependent variable are shown to be identical to those for a multivariate model. An approximaate method of calculating log likelihood ratios, even when all dimensions of the table have more than two levels (no binary variables) is derived. The implications for sociological “causal” models are discussed.     

贝叶斯非线性分层模型在多元索赔准备金评估中的应用

本文将贝叶斯非线性分层模型应用于基于不同业务线的多元索赔准备金评估中,设计了一种合适的模型结构,将非线性分层模型与贝叶斯方法结合起来,应用WinBUGS软件对精算实务中经典流量三角形数据进行建模分析,并使用MCMC方法得到了索赔准备金完整的预测分布。这种方法扩展并超越了已有多元评估方法中最佳估计和预测均方误差估计的研究范畴。在贝叶斯框架下结合后验分布实施推断对非寿险公司偿付能力监管和行业决策具有重要作用。     

Solving generalized multivariate linear rational expectations models

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paper—an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.     

BENCHMARKING LARGE ACCOUNTING FRAMEWORKS: A GENERALIZED MULTIVARIATE MODEL

We present a multivariate benchmarking model for achieving consistency between large quarterly and annual accounting frameworks. The method is based on a quadratic optimization problem, for which many efficient numeric solvers exist. The method combines several features, such as linear constraints, ratio constraints, weights, and inequalities, in one model. Therefore, a wide range of modelling possibilities is supported. This method is especially interesting for national statistical offices, to simplify their processes to achieve consistency between publications.     

Estimation and solution of linear rational expectations models using a polynomial matrix factorization

A method to solve and estimate multivariate linear rational expectations models is described. The method is based on an iterative factorization of the polynomial matrix that describes the lags and expected leads in the model. Our experience is that the method works well in a variety of applications where other methods are either difficult or expensive to use.     

Tests of Normality of Functional Data

The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively used functional data sets and determine which can be treated as normal, possibly after a suitable transformation. We also offer practical guidance on software implementations of all tests we study and develop large sample justification for tests based on sample skewness and kurtosis of functional principal component scores.     

Multivariate analysis: Theory and practice

This paper reviews the problem of analyzing and estimating linear multivariate relationships. A convenient taxonomic framework is established for discussing a variety of multivariate procedures.     

基于C语言数学计算器设计算法探讨

本文讲述了运用C语言来编写求一元二次、一元三次和多元线性方程的解的思路方法。首先对每个功能方法的原理进行阐述,最后我们对计算出来的结果进行了检验。在方程中,我们用到公式法、牛顿切线法、雅可比迭代法和高斯-赛德尔迭代法。     

On equalities of estimations of parametric functions under a general linear model and its restricted models

Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations of matrices and their generalized inverses. In the past several years, a powerful tool—the matrix rank method was utilized to manipulate various complicated matrix expressions that involve generalized inverses of matrices. In this paper, we use this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted model.     

Employee turnover intentions

Most empirical studies testing models of turnover intentions have relied on samples of specific organizations or occupational groups, raising reservations as to the generalizability of their results for broader and more comprehensive populations. To begin to fill this gap, a nearly national sample of employed urban males was utilized and sub–populations were examined in terms of their turnover intentions. A set of biodemographic, organizational, perceptional and job satisfaction variables were incorporated into a multivariate analysis to determine factors best explaining turnover intent. At a second stage, the overall measure of job satisfaction was substituted by four component factors: intrinsic, extrinsic, hygienic and social, which were obtained by a factor analysis of thirteen job satisfaction items. The results of the bivariate and multivariate analysis strongly suggest that specific case findings are congruent with this study's national level of turnover intent. Older age, longer periods of service, lower occupational level were found to have a negative and significant relationship to a worker's intention to change an employer. Intrinsic and hygienic job satisfaction components were found to lead towards a lower intention to leave.     

A Review of Envelope Models

The envelope model was first introduced as a parsimonious version of multivariate linear regression. It uses dimension reduction techniques to remove immaterial variation in the data and has the potential to gain efficiency in estimation and improve prediction. Many advances have taken place since its introduction, and the envelope model has been applied to many contexts in multivariate analysis, including partial least squares, generalised linear models, Bayesian analysis, variable selection and quantile regression, among others. This article serves as a review of the envelope model and its developments for those who are new to the area.     

线性规划在假设开发法中的应用研究

本文尝试运用运筹学中线性规划理论的数学模型,结合SWOT分析决策房地产开发最高最佳使用方式,为开发商或土地估价师提供一条可供参考的技术路线。     

Classification performance of mathematical programming techniques in discriminant analysis: Results for small and medium sample sizes

The performance on small and medium-size samples of several techniques to solve the classification problem in discriminant analysis is investigated. The techniques considered are two widely used parametric statistical techniques (Fisher's linear discriminant function and Smith's quadratic function), and a class of recently proposed nonparametric estimation techniques based on mathematical programming (linear and mixed-integer programming). A simulation study is performed, analyzing the relative performance of the above techniques in the two-group case, for various small sample sizes, moderate group overlap and across six different data conditions. Training samples as well as validation samples are used to assess the classificatory performance of the techniques. The degree of group overlap and sample sizes selected for analysis in this paper are of interest in practice because they closely reflect conditions of many real data sets. The results of the experiment show that Smith's nonlinear quadratic function tends to be superior on the training samples and validation samples when the variances–covariances across groups are heterogeneous, while the mixed-integer technique performs best on the training samples when the variances–covariances are equal, and on validation samples with equal variances and discrete uniform independent variables. The mixed-integer technique and the quadratic discriminant function are also found to be more sensitive than the other techniques to the sample size, giving disproportionally inaccurate results on small samples.     

Generalized variance-ratio tests for serial correlation in multivariate regression models

Exact tests for rth order serial correlation in the multivariate linear regression model are devised which are based on a multivariate generalization of the F-distribution. The tests require the computation of two multivariate regressions. In the special case of a single-equation regression model the procedures reduce to simple always-conclusive F-tests. The tests are illustrated by applications to the Rotterdam Model of consumer demand.     

Exact inference for the difference of Laplace location parameters

We consider exact procedures for testing the equality of means (location parameters) of two Laplace populations with equal scale parameters based on corresponding independent random samples. The test statistics are based on either the maximum likelihood estimators or the best linear unbiased estimators of the Laplace parameters. By conditioning on certain quantities we manage to express their exact distributions as mixtures of ratios of linear combinations of standard exponential random variables. This allows us to find their exact quantiles and tabulate them for several sample sizes. The powers of the tests are compared either numerically or by simulation. Exact confidence intervals for the difference of the means corresponding to those tests are also constructed. The exact procedures are illustrated via a real data example.     

物流配送中心作业流程的统筹优化

针对配送中心作业流程的合理规划问题,对配送中心的作业时序进行分析,寻找每道工序的时差,运用统筹方法中的关键路线法寻找缩短工期的最优方案,建立线性规划模型,计算出最佳作业时序,实现配送中心内部作业优化问题,降低配送中心的运营成本。