偏最小二乘回归分析在研究进出口总额问题中的应用

在经济研究中,自变量之间以及因变量存在着较严重的多重共线性,本文采用偏最小二乘回归来建立多元线性回归模型,以消除多重共线性的影响,从而得到较满意的结果.     

PLSR模型的回归效果分析

本文简单地介绍了多元线性回归、主元回归、部分最小二乘回归模型 ,用实例对三种方法的回归性能进行比较 ,并指出在消除多重共线性、回归系数估计精度及预测精度等方面 ,部分最小二乘回归模型优于其它两种模型     

岭回归和核主成分回归在消除共线性中的实证分析及比较

检测和解决多元回归分析中的多重共线性问题具有重要意义.本文采用岭回归(RR)和核主成分回归(KCPR)对同一数据进行回归分析,使用方差膨胀因子(VIF)和条件指数(CI)作为共线性诊断的量度,并对回归模型结果进行比较.经过实证分析,发现这两种回归方法都能很好地消除多重共线性,总的来说核主成分回归的对内拟合效果要优于岭回归.但是这两种方法的参数选择的不同对回归模型的好坏都有巨大影响,需要进一步分析判断.     

基于多重共线性的处理方法

多重共线性简称共线性是多元线性回归分析中一个重要问题。消除共线性的危害一直是回归分析的一个重点。目前处理严重共线性的常用方法有以下几种:岭回归、主成分回归、逐步回归、偏最小二乘法、Lasso回归等。本文就这几种方法进行比较分析,介绍它们的优缺点,通过实例分析以便于选择合适的方法处理共线性。     

苏州外资制造业经济增长因素贡献率测算模型与分析

在经济增长因素分析中,人们常用生产函数来分析经济增长过程,测算各要素对经济增长的贡献率.本文利用柯布-道格拉斯生产函数给出苏州外资制造业经济增长的六个影响因素贡献率测算模型与分析,由于六个影响因素之间存在多重共线性,为消除多重共线性,使模型合理,本文使用主成分回归建立模型,结果令人满意。     

PLS回归在国际机场服务改进中的应用

为了帮助国际机场在资源有限的情况下,明确服务改进方向从而实现服务质量的改善,本文在现有调查数据的基础上,建立了一个能够明确机场各项服务对“旅客总体满意度”直接影响程度的模型,并给出了运用此模型的诊断思路和方法。鉴于建模目的需要以及对消除多重共线性方法的对比分析,本文选用了偏最小二乘(PLS)回归分析方法。最后对其中一个国际机场进行了诊断,指出了机场服务改进的方向。     

基于主成分回归的杭州市PM2.5含量的综合分析

为探究杭州市PM2.5含量与其他指标之间的关系,搜集杭州市2019年的AQI指数和AQI 6项指标进行分析.首先通过相关分析揭示PM2.5与其余5项指标的相关性,发现各指标与PM2.5均呈线性关系,又因为其余5项指标之间存在显著的线性相关性,故自变量之间存在多重共线性.为了消除多重共线性的影响,对这5项指标提取主成分,再基于主成分分析做回归分析.最后对模型进行统计诊断,按照一定标准筛选出原始数据中的强影响点,删除强影响点后得到最终模型.     

偏最小二乘建模在R软件中的实现及实证分析

通过介绍偏最小二乘（PLS）的建模和显著性检验原理,解决了小样本多变量且变量间存在多重共线性的回归问题,建立了多变量对多变量的回归模型,并使用R软件（版本为Ri3862．15．1）实现了PLS建模;最后基于葡萄和葡萄酒理化指标数据进行了实证分析．     

微观数据和宏观汇总数据在统计分析上的差异——以C-D生产函数为例

基于2008年经济普查的数据,从描述统计分析和回归分析两方面分别对微观数据和宏观汇总数据在统计分析上的差异进行了实证分析.在描述统计分析中发现,宏观汇总数据比微观数据更接近正态分布,但对数化处理后的数据并非如此;在回归分析中发现,基于微观数据和宏观汇总数据估计的生产函数,在消除异方差和多重共线性之前,无论是在生产函数的规模效应、生产要素的贡献率以及生产要素对产出的解释力度上均存在着差异,但是在消除异方差和多重共线性之后,在要素对产出的解释力度上仍存在很大差异.     

PLS1回归对多变量信息的综合与筛选作用分析

王惠文，ＰＬＳ１回归对多变量信息的综合与筛选作用分析，数理统计与管理，１９９８，１７（４），４６～４９。本文讨论了ＰＬＳ１回归对多变量系统中的信息进行综合与筛选的工作策略。通过例证分析指出，ＰＬＳ１回归方法可以有效地提取对系统解释性最强的综合变量，排除重叠信息或无解释意义的信息干扰，从而较好地克服变量多重相关性在系统建模中的不良作用     

Modelling LGD for unsecured personal loans: decision tree approach

The New Basel Accord, which was implemented in 2007, has made a significant difference to the use of modelling within financial organisations. In particular it has highlighted the importance of Loss Given Default (LGD) modelling. We propose a decision tree approach to modelling LGD for unsecured consumer loans where the uncertainty in some of the nodes is modelled using a mixture model, where the parameters are obtained using regression. A case study based on default data from the in-house collections department of a UK financial organisation is used to show how such regression can be undertaken.     

Regression-fuzzy approach to land valuation

In this paper, we demonstrate that the fuzzy pricing model can improve regression analysis in applications where non-smoothness appears. Combining the fuzzy and regression approaches it is capable of modelling complex non-linearities. The application of this approach describes an effort to design a regression-fuzzy system to estimate real estate market values, especially for vacant urban plots. The results are compared with those obtained using a traditional multiple regression model only. The changes of parameters in the domain of independent variables of the regression function are determined by the analysis of membership functions defining the terms of the fuzzy model. The paper also describes possible future research. The suggested method is interesting for real estate appraisers, real estate companies, and bureaus because it provides a better overview of location prices. The suggested approach could be also used in various other economic and business analyses.     

Bayesian estimation of NIG models via Markov chain Monte Carlo methods

The normal inverse Gaussian (NIG) distribution is a promising alternative for modelling financial data since it is a continuous distribution that allows for skewness and fat tails. There is an increasing number of applications of the NIG distribution to financial problems. Due to the complicated nature of its density, estimation procedures are not simple. In this paper we propose Bayesian estimation for the parameters of the NIG distribution via an MCMC scheme based on the Gibbs sampler. Our approach makes use of the data augmentation provided by the mixture representation of the distribution. We also extend the model to allow for modelling heteroscedastic regression situations. Examples with financial and simulated data are provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Exploring the model development process in discrete-event simulation: insights from six expert modellers

This paper explores the model development process in discrete-event simulation (DES) by reporting on an empirical study that follows six expert modellers while building simulation models. DES is a widely used modelling approach, however little is known about the modelling processes and methodology adopted by modellers in practice. Verbal Protocol Analysis is used to collect data, where the participants are asked to speak aloud while modelling. The results show that the expert modellers spend a significant amount of time on model coding, verification and validation, and data inputs. The modellers iterate often between modelling activities. Patterns of modelling behaviour are identified, suggesting that the modellers adopt distinct modelling styles. This study is useful in that it provides an empirical view of existing DES modelling practice, which in turn can inform existing research and simulation practice as well as teaching of DES modelling to novices.     

Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal.An iterative weighted partial spline least squares estimator(IWPSLSE)for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE)with weights constructed by using the within-group partial spline least squares residuals in the sense     

Heteroscedastic Laplace mixture of experts regression models and applications

Mixture of Experts(MoE) regression models are widely studied in statistics and machine learning for modeling heterogeneity in data for regression, clustering and classification.Laplace distribution is one of the most important statistical tools to analyze thick and tail data. Laplace Mixture of Linear Experts(LMoLE) regression models are based on the Laplace distribution which is more robust. Similar to modelling variance parameter in a homogeneous population, we propose and study a new novel class of models: heteroscedastic Laplace mixture of experts regression models to analyze the heteroscedastic data coming from a heterogeneous population in this paper. The issues of maximum likelihood estimation are addressed. In particular, Minorization-Maximization(MM) algorithm for estimating the regression parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo simulations. Results from the analysis of two real data sets are presented.     

Multivariate Local Polynomial Fitting for Martingale Nonlinear Regression Models

Local polynomial modelling is a useful tool for nonlinear time series analysis. For nonlinear regression models with martingale difference errors, this paper presents a simple proof of local linear and local quadratic fittings under apparently minimal short-range dependence condition. Explicit formulae for the asymptotic bias and asymptotic variance are given, which facilitate numerical evaluations of these important quantities. The general theory is applied to nonparametric partial derivative estimation in nonlinear time series. A bias-adjusted method for constructing confidence intervals for first-order partial derivatives is described. Two examples, including the sunspots data, are used to demonstrate the use of local quadratic fitting for modelling and characterizing nonlinearity in time series data.     

Rank estimation in reduced-rank regression

Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained.