具有非参数AR(1)误差的回归模型的局部线性估计

考虑随机设计下具有一阶非参数自回归误差的线性回归模型,构造了参数和非参数函数的局部线性估计。在适当的条件下,证明了参数估计量的渐近正态性,并给出了非参数函数估计的收敛速度。模拟算例表明局部线性方法优于核方法。     

部分变量带误差的线性函数关系模型的参数估计及相合性

本文讨论了部分变量带误差的线性函数关系模型的参数估计问题，在较弱条件下证明了所获得的估计的强相合性，并给出了收敛速度。     

多维门限自回归模型参数估计的渐近正态性

对多维门限自回归模型的参数估计，宋心远等在1990年给出了自回归系数矩阵最小二乘估计的强相容性，由此进一步得到了此估计的渐近正态性。     

CES生产函数模型的修正及实证分析

在经济增长因素分析中,利用CES生产函数模型测算各影响要素对经济增长的贡献率是人们常常研究的重要课题.本文引进虚拟变量,提出CES生产函数的修正模型,并给出模型非线性回归的参数估计方法.在应用修正的CES生产函数模型测算要素贡献率上,传统的方法误差较大.针对该问题,本文给出新的准确测算要素贡献率的方法.最后给出中国经济增长要素贡献率实证分析,效果良好,结果符合实际.     

新高阶多变量马尔可夫模型（英文）

本文提出了一种新高阶多变量马尔可夫模型,并对其收敛性进行了分析.给出了模型的参数估计方法.数值实验表明在预测精度方面新高阶多变量马尔可夫模型比高阶多变量马尔可夫模型更加有效.     

新高阶多变量马尔可夫模型

本文提出了一种新高阶多变量马尔可夫模型,并对其收敛性进行了分析.给出了模型的参数估计方法.数值实验表明在预测精度方面新高阶多变量马尔可夫模型比高阶多变量马尔可夫模型更加有效.     

基于梯度提升回归树的冷水机组能耗预测方法

冷水机组作为空调系统最主要的能耗设备,建立冷水机组能耗预测模型对于节能运行优化具有重要意义。本文针对冷水机组运行参数繁多,能耗预测模型超参数难以调优等特点,提出了基于梯度提升回归树的冷水机组能耗预测方法,并利用冷水机组实测数据对模型进行了训练与验证,同时对比了支持向量回归和决策树模型。结果表明:基于梯度提升回归树的能耗预测模型能够更准确的预测冷水机组能耗。对比其他两种模型,MAE和RMSE分别平均降低了24.5%和45.5%,相关系数达到0.999 7,并且模型对超参数不敏感,能够在较宽泛的范围内比较好地拟合数据,具有较高的实用价值。     

基于GM-噪声SVR方法的矿山设备可靠性参数估计

为了有效估计小子样条件下矿山设备的三参数威布尔分布可靠性模型参数,提出基于GM-噪声SVR的参数估计方法。该方法以灰色估计法(GM)为基础估计模型的位置参数,采用基于训练样本数量和噪声参数寻优的ε - 带支持向量回归机(ε-SVR)估计尺度参数和形状参数,并通过拟合的三参数威布尔分布函数分析预测和解决设备的可靠性问题。算例结果表明,GM-噪声SVR方法可以很好地用于矿山设备可靠性模型参数估计,估计某带式输送机三参数威布尔分布可靠性模型的位置参数、尺度参数和形状参数依次为3.1525、188.3763、1.0476,平均无故障时间为188 h,标准均方根误差NRMSE为0.0519。这表明该方法的可行性和有效性。     

基于M-SCAD方法的利率期限结构中的节点选择

针对国债市场部分债券价格扭曲的情况,提出一种基于M-SCAD(M-Estimator Smoothing Clipped Absolute Deviation)方法的稳健样条利率期限结构模型.首先,将M-SCAD方法引入到三次多项式样条函数中对利率期限结构建模.然后,给出模型的优点和性质,使用该方法进行节点选择,可以确定样条函数的节点数量和位置,同时进行参数估计.最后,把构建的模型进行实证研究,对上海证券交易所交易的国债利率期限结构进行建模分析.样本外预测结果显示:与传统的方法相比,新方法可以有效地选择合适的模型,增加参数估计的稳健性,提高预测的精度,增强期限结构定价的准确度.     

噪声因子存在下的多响应参数设计的优化

采用多元损失函数法,对噪声因子存在下的多响应稳健性参数设计进行了优化.该方法考虑了噪声因子的影响,结合响应期望值和响应方差,其中响应方差结合了噪声因子产生的方差和拟合模型的预测方差,给出了综合方差的无偏估计,使解决方案对噪声因子和参数估计的不确定性都具有稳健性,避免了方差出现非正定的可能性.采用该方法对实例进行分析,得到较好的优化结果.     

A genetic programming based fuzzy regression approach to modelling manufacturing processes

Fuzzy regression has demonstrated its ability to model manufacturing processes in which the processes have fuzziness and the number of experimental data sets for modelling them is limited. However, previous studies only yield fuzzy linear regression based process models in which variables or higher order terms are not addressed. In fact, it is widely recognised that behaviours of manufacturing processes do often carry interactions among variables or higher order terms. In this paper, a genetic programming based fuzzy regression GP-FR, is proposed for modelling manufacturing processes. The proposed method uses the general outcome of GP to construct models the structure of which is based on a tree representation, which could carry interaction and higher order terms. Then, a fuzzy linear regression algorithm is used to estimate the contributions and the fuzziness of each branch of the tree, so as to determine the fuzzy parameters of the genetic programming based fuzzy regression model. To evaluate the effectiveness of the proposed method for process modelling, it was applied to the modelling of a solder paste dispensing process. Results were compared with those based on statistical regression and fuzzy linear regression. It was found that the proposed method can achieve better goodness-of-fitness than the other two methods. Also the prediction accuracy of the model developed based on GP-FR is better than those based on the other two methods.     

Factor complexity of crash occurrence: An empirical demonstration using boosted regression trees

Factor complexity is a characteristic of traffic crashes. This paper proposes a novel method, namely boosted regression trees (BRT), to investigate the complex and nonlinear relationships in high-variance traffic crash data. The Taiwanese 2004–2005 single-vehicle motorcycle crash data are used to demonstrate the utility of BRT. Traditional logistic regression and classification and regression tree (CART) models are also used to compare their estimation results and external validities. Both the in-sample cross-validation and out-of-sample validation results show that an increase in tree complexity provides improved, although declining, classification performance, indicating a limited factor complexity of single-vehicle motorcycle crashes. The effects of crucial variables including geographical, time, and sociodemographic factors explain some fatal crashes. Relatively unique fatal crashes are better approximated by interactive terms, especially combinations of behavioral factors. BRT models generally provide improved transferability than conventional logistic regression and CART models. This study also discusses the implications of the results for devising safety policies.     

Analysis of traffic injury severity: an application of non-parametric classification tree techniques

Statistical regression models, such as logit or ordered probit/logit models, have been widely employed to analyze injury severity of traffic accidents. However, most regression models have their own model assumptions and pre-defined underlying relationships between dependent and independent variables. If these assumptions are violated, the model could lead to erroneous estimations of injury likelihood. The classification and regression tree (CART), one of the most widely applied data mining techniques, has been commonly employed in business administration, industry, and engineering. CART does not require any pre-defined underlying relationship between target (dependent) variable and predictors (independent variables) and has been shown to be a powerful tool, particularly for dealing with prediction and classification problems. This study uses the 2001 accident data for Taipei, Taiwan. A CART model was developed to establish the relationship between injury severity and driver/vehicle characteristics, highway/environmental variables and accident variables. The results indicate that the most important variable associated with crash severity is the vehicle type. Pedestrians, motorcycle and bicycle riders are identified to have higher risks of being injured than other types of vehicle drivers in traffic accidents.     

Convergence in Nonlinear Regression

Least squares estimates of parameters of a multiple linear regression model are known to be highly variable when the matrix of independent variables is near singular. Using the latent roots and latent vectors of the “correlation matrix” of the dependent and independent variables a modified least squares estimation procedure is introduced. This technique enables one to determine whether the near singularity has predictive value and examine alternate prediction equations in which the effect of the near singrtlarity has been removed from the estimates of the regression coefficients. In addition a method for performing backward elimination of variables using standard least squares or the modified procedure is presented.     

Sparse multivariate regression with missing values and its application to the prediction of material properties

In the field of materials science and engineering, statistical analysis and machine learning techniques have recently been used to predict multiple material properties from an experimental design. These material properties correspond to response variables in the multivariate regression model. In this study, we conduct a penalized maximum likelihood procedure to estimate model parameters, including the regression coefficients and covariance matrix of response variables. In particular, we employ $l_1$-regularization to achieve a sparse estimation of The regression coefficients and inverse covariance matrix of response variables. In some cases, there may be a relatively large number of missing values in the response variables, owing to the difficulty of collecting data on material properties. We therefore propose a method that incorporates a correlation structure among the response variables into a statistical model to improve the prediction accuracy under the situation with missing values. The expectation maximization algorithm is also constructed, which enables application to a dataset with missing values in the responses. We apply our proposed procedure to real data consisting of 22 material properties.     

Predicting crash risk and identifying crash precursors on Korean expressways using loop detector data

In order to improve traffic safety on expressways, it is important to develop proactive safety management strategies with consideration for segment types and traffic flow states because crash mechanisms have some differences by each condition. The primary objective of this study is to develop real-time crash risk prediction models for different segment types and traffic flow states on expressways. The mainline of expressways is divided into basic segment and ramp vicinity, and the traffic flow states are classified into uncongested and congested conditions. Also, Korean expressways have irregular intervals between loop detector stations. Therefore, we investigated on the effect and application of the detector stations at irregular intervals for the crash risk prediction on expressways. The most significant traffic variables were selected by conditional logistic regression analysis which could control confounding factors. Based on the selected traffic variables, separate models to predict crash risk were developed using genetic programming technique. The model estimation results showed that the traffic flow characteristics leading to crashes are differed by segment type and traffic flow state. Especially, the variables related to the intervals between detector stations had a significant influence on crash risk prediction under the uncongested condition. Finally, compared with the single model for all crashes and the logistic models used in previous studies, the proposed models showed higher prediction performance. The results of this study can be applied to develop more effective proactive safety management strategies for different segment types and traffic flow states on expressways with loop detector stations at irregular intervals.     

使用回答概率的回归插补

对于缺失数据,本文根据目标变量和辅助变量的无回答者总体总量的无偏估计,利用再抽样(复制)技术,构造了使用回答概率的回归插补;进而,利用再抽样(复制)技术,得到了该插补估计的方差估计;并进行了大量模拟,模拟结果表明使用回答概率的回归插补估计及其方差估计具有良好的性质。     

Visualizable and interpretable regression models with good prediction power

Many methods can fit models with a higher prediction accuracy, on average, than the least squares linear regression technique. But the models, including linear regression, are typically impossible to interpret or visualize. We describe a tree-structured method that fits a simple but nontrivial model to each partition of the variable space. This ensures that each piece of the fitted regression function can be visualized with a graph or a contour plot. For maximum interpretability, our models are constructed with negligible variable selection bias and the tree structures are much more compact than piecewise-constant regression trees. We demonstrate, by means of a large empirical study involving 27 methods, that the average prediction accuracy of our models is almost as high as that of the most accurate “black-box” methods from the statistics and machine learning literature.     

多元线性回归分析在工业洗涤机械行业发展趋势预测中的应用

指出了工业洗涤机械行业发展趋势量化预测的必要性,提出了回归分析在行业发展趋势预测中的应用步骤,建立了我国工业洗涤机械发展趋势预测的多元线性回归模型。在模型讨论中,利用经济学中的需求函数,提炼出解释变量。根据大量调查数据,利用Excel统计软件进行了相关分析、回归分析和统计检验。最后,运用所建立的多元线性回归预测模型对工业洗涤机械行业在2004年的需求量进行了预测。     

半相依回归模型参数的协方差改进估计

本文研究了两个半相依回归系统的未知回归系数的估计问题。本文首先给出一种基于方差分量限定估计的两步协方差改进估计,并且给出了均方误差意义下优于最小二乘估计的条件。对于基于方差分量非限定估计的两步协方差改进估计,利用服从Wishart分布随机变量的可加性,本文给出了一种全新的估计形式,并且证明了该估计较文献中给出的两步协方差改进估计更加有效。