城市道路短时交通流量预测

结合BP神经网络模型和自回归求和滑动平均(ARIMA)模型对城市道路交通短时区间流量进行预测.影响交通流的因素有很多,难以一一量化,但这些因素都可以由线性自相关结构和非线性结构结合线性组合得到.而BP神经网络对非线性关系有很好的拟合效果,ARIMA模型则具有良好的线性拟合能力.在训练模型时,先用ARIMA模型拟合训练集,与原始数据作差得到一组残差;用BP神经网络模型拟合残差;将两个模型结合得到组合模型.将2017年7月1日7:00到2017年7月1日18:00期间,贵阳市某个路口断面所采集的过车数据作为训练集,建立ARIMA模型和BP神经网络模型以及组合模型,预测2017年7月1日18:00到2017年7月1日19:00的短时交通流.过车数据统计时间间隔为5min,则训练集共有有效数据132组,测试集的有效数据为12组.分别用三类误差分析指标比较三个模型的拟合、预测效果,结果显示组合模型的预测效果比两个模型单独使用的预测效果更准确.     

二个四参数增长曲线模型参数初始值的确定方法与模型应用

对非线性回归模型进行非线性最小二乘估计一般需要确定参数初始值.在非线性回归模型中,General Logistic模型和Von Bertalanffy模型是二个含有四参数的增长曲线模型,对数据的拟合有较强的适应性,应用较为广泛.本文给出这两个模型参数初始值的确定方法,并应用于实际拟合,得到很好的效果.     

海南人口增长模型的统计分析

介绍了求非线性回归模型参数的基本理论,并且以海南人口增长数据为例,对比_分析了利用Malthus模型和Logistic回归模型的模拟结果.利用Mathematica软件绘制了海南人口增长数据的点图.最后给出海南人口增长数据的拟合曲线和置信域的图形.     

零膨胀集群数据层次回归模型的贝叶斯推断

零膨胀Poisson回归模型是研究零观测值过多的计数数据的常用工具,本文提出了一类拟合具有这类特征的集群数据的层次零膨胀泊松回归模型,并给出了相应的贝叶斯推断方法,参数估计通过Gibbs抽样获得,模型比较与选择则通过拟合优度检验与BIC准则实现.最后,利用一个船舶受损事故数据来展示本文方法的实现及应用.     

总体最小二乘准则下非线性EV模型的参数拟合方法

在非线性回归模型参数拟合问题中,当数据中的每个变量都存在不可忽略的误差时,在普通的最小二乘准则下拟合出的参数不是最优的.按照总体最小二乘准则,以观测点到拟合曲线或拟合曲面垂直距离平方和为目标函数,然后用最优化方法搜索出使目标函数值取最小值的参数和数据点估计,从而给出求最优模型参数的算法,最后,通过计算机仿真和与文献比较,验证了提出方法的正确性.     

航空发动机环形燃烧室噪声总声级多元回归模型研究

本文利用航空发动机环行燃烧室测试数据 ,采用线性回归和非线性回归两种方法分别得到了燃烧室噪声总声级和燃烧噪声峰值及峰值频率的拟合模型 ,并利用线性回归模型由燃烧室外部测量结果估算燃烧室内部总声级 ,所提供的噪声数据可供研究发动机燃烧室结构完整性和可靠性时参考 .     

Beta模型的柔性扩展与洛伦兹曲线拟合优化

在传统Beta模型基础上,采取与e指数n次多项式函数乘积方式,构造了一种参数可有限扩展的线性模型——Beta柔性扩展模型.据对全国数学建模分组数据的拟合实验,该模型的均方误差达到10^-9数量级水平.对19个国家收入分配分组数据进行多个模型的估计误差对比,证明该模型的拟合质量总体上优于对比模型.探索性提出的“固定参数+柔性参数”线性建模方式和“递次回归、择优筛选”的分组数据逼近机制,为提高洛伦兹曲线拟合精度提供了一种可参考的新方法、新选择.     

上海证券市场回报率分析——基于ARIMA模型和GARCH模型

本文分析中国上海证券市场回报率。分别通过APdMA模型和GARCH模型，发现若用APdMA模型分析和建立时间序列模型，一次自回归项是不够的，需要高次项，在大多数情形，若运用GARCH模型，则GARCH（1，1）就能够很好的拟合数据。     

上海世博会的经济综合影响力指数模型

分析上海世博会在世博筹备建设和举办时期对上海市经济方面影响.筛选了世博会影响经济的四个方面(国民经济,财政收支,固定资产投资和对外经济贸易与旅游)的10个主要指标,构建了世博会影响经济的评价指标体系,针对每一项指标,利用1995年到2002的实际数据用指数回归拟合模型测算出2003-2010年在未筹办世博会情况下各项经济指标的估计(拟合)数据,并建立单指标的影响力指数模型,在分析2003年后的实际数据与拟合数据差异基础上,获得了上海世博会在每个指标方面对上海的影响力指数;建立了多指标综合影响力指数模型,得出总的经济影响力的指数为0.2403.考虑到2008年底金融危机势必会削弱世博会对经济的影响,通过参照另外两个同为中国直辖市的重庆和天津相同指标的变化,运用单独建立的模型,剔除金融危机对经济的影响,从而获得更客观地揭示世博对上海地区经济的真实影响程度.并就两个典型的指标给出了具体的演算过程,最后得到了消除了金融危机后的所有指标的影响力指数值,最终获得总的经济影响力的指数为0.2531,即世博会对上海市经济的实际贡献率为25.31%.     

跟踪雷达测量误差的统计模型(Ⅰ):模型的建立

本文提出以如下具有慢时变万差的线性回归－自回归混合模型用于描述跟踪雷达测量误差的变化规律，并提出了模型个数的估计方法．数值例子表明，本文提出的模型能较好地拟合跟踪雷达误差数据．     

上海市工业废水排放量的多元非线性回归预测

根据2000年至2009年上海市的人均生产总值和工业重复用水量并结合工业废水排放量的资料,构建了一种基于时间序列的多元非线性回归预测模型,并进行了评估和分析.模型具有较高的拟合精度,能客观反映工业废水的排放量,可以为决策者提供参考,提高相关部门的管理水平.     

基于时间序列建模和控制图的异常交易检测方法

可疑交易识别是打击洗钱犯罪所要面对的一项重要任务.为辅助反洗钱分析人员从海量金融交易信息中甄别客户异常交易,本文提出一种新的基于非线性马尔科夫随机过程、相空间重构和隐马尔科夫链的非线性随机方法,用于对金融交易时序进行建模拟合,然后应用鲁棒控制图对估计误差进行检验以发现异常.应用该算法对实际交易数据和仿真数据的分析验证了所提方法的有效性和可行性,可以被用于异常交易的监测.     

基于LS-SVM的管道腐蚀速率灰色组合预测模型

为提高管道腐蚀速率预测精度,建立了一种基于最小二乘支持向量机的灰色组合预测模型.以各种灰色模型对管道腐蚀速率的预测结果作为支持向量机的输入,以管道腐蚀速率的实测值作为支持向量机的输出,采用最小二乘支持向量机回归算法和高斯核函数对支持向量机进行训练,利用训练好的支持向量机进行组合预测.预测模型兼具灰色模型所需原始数据少、建模简单、运算方便的优势和最小二乘支持向量机具有泛化能力强、非线性拟合性好、小样本等特性,弥补了单一预测模型的不足,避免了神经网络组合预测易于陷入局部最优的弱点.模型结构简单、实用,仿真结果验证了其有效性.     

Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression

Continuous threshold regression is a common type of nonlinear regression that is attractive to many practitioners for its easy interpretability. More widespread adoption of threshold regression faces two challenges: (i) the computational complexity of fitting threshold regression models and (ii) obtaining correct coverage of confidence intervals under model misspecification. Both challenges result from the nonsmooth and nonconvex nature of the threshold regression model likelihood function. In this article we first show that these two issues together make the ideal approach for making model-robust inference in continuous threshold linear regression an impractical one. The need for a faster way of fitting continuous threshold linear models motivated us to develop a fast grid search method. The new method, based on the simple yet powerful dynamic programming principle, improves the performance by several orders of magnitude. Supplementary materials for this article are available online.     

Application in stochastic volatility models of nonlinear regression with stochastic design

In regression model with stochastic design, the observations have been primarily treated as a simple random sample from a bivariate distribution. It is of enormous practical significance to generalize the situation to stochastic processes. In this paper, estimation and hypothesis testing problems in stochastic volatility model are considered, when the volatility depends on a nonlinear function of the state variable of other stochastic process, but the correlation coefficient |ρ|≠±1. The methods are applied to estimate the volatility of stock returns from Shanghai stock exchange. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of strategies when building linear prediction models

In statistical and biometric sciences, one often uses predictive linear models. The initial form of such models is usually obtained by fitting the coefficients of the model to a set of observed data according to the classical least squares method. Newborn models that are obtained in this way will be referred to as raw models. Such raw models are often subject of efforts to improve them as to their predictive performance on external datasets. Several methods can be followed to fine‐tune raw models, thus leading to a variety of model building strategies. In this paper, the idea of so‐called victory rates is introduced to compare the performance of building strategies mutually.Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

A unified method to calculate the moments of the least squares estimators in nonlinear regression

A unified method and a set of regularity conditions are presented in this paper to calculate the moments of the least squares estimators, residuals, and fitting errors in nonlinear regression. The results given by Box, Clarke and other authors have been greatly improved and developed. The key point of the method is that we find a series of stochastic expansions related to the estimators. These expansions consist of curvature measures and independent standard normal random variables; therefore they are easy to understand and to deal with from statistical and geometrical point of view.The project is supported by The National Natural Science Foundation of China.