变系数空间自回归模型的Bootstrap检验

变系数空间自回归模型是变系数模型在空间数据分析方面的推广,因其众多的应用背景而得到广泛的重视和研究,确认模型中系数是否真正随变量的变化而变化是应用变系数空间自回归模型需解决的首要问题.本文基于Bootstrap检验方法研究了变系数空间自回归模型中的常系数项的辨别问题,为建立半变系数空间自回归模型提供依据.最后,通过模拟...     

半变系数模型的M估计

本文讨论半变系数模型的稳健M估计.先用局部线性方法给出未知可测函数的一步估计,并讨论其弱一致性和渐近正态性;通过Back-fitting技巧,给出未知参数向量的一般M估计,然后再通过局部M方法给出未知函数的两步估计,并讨论它们的渐近正态性.     

基于系数估计的趋势性分析检验变系数模型中的不变系数

当应用半变系数模型分析数据时,应首先确定哪些系数为常值,哪些系数随因素而变化。本文通过对变系数模型中的系数的局部线性估计进行再光滑,基于其变化的趋势性构造统计量以检验其中的常值系数,为半变系数模型的建立提供理论依据。并通过数值模拟试验考察了检验的功效,得到了满意的结果。     

响应变量随机缺失下的变系数部分线性模型的经验似然推断

本文考虑了响应变量随机缺失下的变系数部分线性模型的估计问题。利用经验似然方法,给出了参数部分的调整经验似然比函数,证明其渐近服从标准卡方分布。进而构造了参数部分的置信域,得到了其极大经验似然估计的最优参数收敛速度和渐近半参数有效界。模拟结果表明调整经验似然方法优于未调整的经验似然方法。     

变系数广义KdV方程的精确类孤子解

本文主要研究了变系数广义KdV方程的精确解。利用一种函数变换将变系数KdV方程约化为非线性常微分方程，借助于Mathematica软件求出该类方程的几种精确解。通过数值实例说明了方法的有效性，为变系数Kdv方程在自然科学领域的应用提供了理论依据。     

有约束的混合系数线性模型参数的估计

提供了在连续测量数据的背景情况下，给出了线性模型：{Zi=Xia Yiβi εi i=1,2,……，m βi^i.i.d.～（b,∑）εi^i.i.d.～（0,σ^2Ini)具有约束H（a‘,b‘)‘=0时，固定系数a和随机系数β的一种估计，并讨论了该估计的性质。     

空化模型中的相变系数影响研究

利用数值计算的方法,对空化模型中的相变系数进行研究.将数值计算和实验数据进行分析和整理,分别获得蒸发系数和冷凝系数与空化数之间的依赖关系.通过比较半球头圆柱体的二维轴对称模型数值计算结果表明:不同空化数对应着不同相变系数.其中,蒸发系数和冷凝系数分别对主空泡、次生空泡、尾空泡等类型的空泡在形态、溃灭位置、溃灭强度等方面有较大影响.     

二维变系数抛物型方程高精度恒稳定的改进的Douglas格式

本文将算子方法和粘结系数方法相结合,构造出了求二维变系数抛物型方程的改进的Douglas格式,格式的截断误差阶达O(τ2+h4),并用Fourier分析方法讨论了格式的绝对稳定性.文末给出的数值例子表明了本文理论分析的正确性和所构造格式的有效性及优越性.长期以来,现有关于抛物型方程的差分格式都是对常系数方程而言的,本文较简便的给出了二维情形下变系数抛物型方程的差分解法,此方法完全可以推广到高维情形.     

钴湿法冶炼萃取过程质量指标的软测量

利用基于物料衡算关系的机理模型、基于萃取平衡关系的半经验模型以及基于径向基函数-偏最小二乘法的萃余液的pH值预测模型,提出了一种钴湿法冶炼萃取过程质量指标软测量建模方法.机理模型用以描述过程的整体特性;半经验模型利用拟牛顿变尺度方法对其中未知参数进行估计,并用以逼近机理模型中的萃取平衡关系;基函数-偏最小二乘法则用来预测萃余液pH值.将所建立的软测量模型应用于实际钴湿法冶炼生产过程中,结果表明,该方法具有良好的预测精度.     

基于POT法确定风压系数极值的自动阈值选取与参数估计EI北大核心CSCD

风压系数极值是确定建筑围护结构设计风荷载的重要变量。实现阈值自动选取和合适的模型参数估计方法是保证超阈值模型极值计算结果精确性的先决条件,也是当前超越阈值模型研究的热点和难点。以CAARC高层建筑刚性模型测压风洞试验数据为基础开展超越阈值模型极值计算方法研究,通过对独立峰值数量和相关性研究独立峰值提取方法的性能;采用蒙特卡罗法研究4种不同的广义Pareto分布参数估计方法的性能,给出最佳参数估计方法选择建议;提出基于形状参数或极值估计结果稳定性的变点-局部比较阈值自动选取新方法。研究结果表明,基于变点理论-形状参数/极值稳定性阈值自动选取方法具有较小的样本依赖性,以及有较好的样本非高斯适用性,由此构建的改进超越阈值模型计算风压系数极值与标准极值的偏差小于5%,且完全实现阈值客观、自动选取,研究结论完善了小样本风压系数极值估计方法,对确定建筑围护结构设计风荷载具有重要意义,且可推广到其他极值估计领域。     

Problems of Nonnormality and Multicollinearity for Forecasting Methods Based on Least Squares

Many popular forecasting and time-series analysis methods assume that the variable to be forecast can be expressed as a linear function of a set of predictors. The predictors may include variables related in either a correlative or causal fashion to the response variable, lagged values of this variable, or known mathematical functions of time. The method of least squares is used almost exclusively to estimate the parameters in these models. This paper discusses two hazards in the indiscriminant use of least squares; nonnormality of the observations on the variable of interest and multicollinearity among the predictors. Robust estimation methods are suggested as alternatives to least squares for nonnormal data, and a robust version of exponential smoothing is developed. A small Monte Carlo study indicates that the robust procedure can be superior to ordinary exponential smoothing in many situations. The sources and effects of multicollinearity are discussed, and several diagnostic statistics are presented. Methods for dealing with multicollinearity are reviewed, including collecting additional data, variable selection, and biased estimation. An example of ridge regression is included.     

Monitoring General Linear Profiles When Random Errors Have Contaminated Normal Distributions

We consider the quality of a process which can be characterized by a general linear profile where the random error has a contaminated normal distribution. On the basis of trimmed least squares estimation, new control charts for monitoring the coefficient parameters and/or the error variance of the profile are proposed. Simulation studies show that the proposed control charts outperform the existing competitors under such a profile. An example from manufacturing facility is used to illustrate the applicability of the proposed charts. Copyright © 2013 John Wiley & Sons, Ltd.     

基于改进粒子群算法的最小二乘影响系数法的理论及实验研究

针对最小二乘影响系数法平衡过程中出现的某些测点残余振动较大及平衡质量较大等问题,将一种基于遗传交叉因子改进的粒子群算法引入到转子动平衡最小二乘影响系数法中。实例计算说明改进后的算法具有很好收敛特性和全局搜索能力,与基本最小二乘影响系数法计算结果相比,有效降低最大配重质量和最大残余振动大小。通过实验验证了结果的正确性和方法的可行性。     

Optimization of informative spectral variables for the quantification of EGCG in green tea using Fourier transform near-infrared (FT-NIR) spectroscopy and multivariate calibration

Epigallocatechin-3-gallate (EGCG) is credited with the majority of the health benefits associated with green tea consumption. It has a high economic and medicinal value. The feasibility of using different variable selection approaches in Fourier transform near-infrared (FT-NIR) spectroscopy for a rapid and conclusive quantitative determination of EGCG in green tea was investigated. Graphically oriented multivariate calibration modeling procedures such as interval partial least squares (iPLS), synergy interval partial least squares (siPLS), and genetic algorithm optimization combined with siPLS (siPLS-GA) were applied to select the most efficient spectral variables that provided the lowest prediction error. The performance of the final model was evaluated according to the root mean square error of prediction (RMSEP) and coefficient of determination (R(2)) for the prediction set. Experimental results showed that the siPLS-GA model obtained the best results in comparison to other models. The optimal models were achieved with R(2)(p) = 0.97 and RMSEP = 0.32. The model can be obtained with only 36 variables retained and it provides a robust model with good estimation accuracy. This demonstrates the potential of NIR spectroscopy with multivariate calibration methods to quickly detect the bioactive component in green tea.     

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。     

An Adaptive Estimation Algorithm

An adaptive approach for sequential parameter-change detection and revision of the moving average parameter in the first-order integrated-moving average time series model is presented. Derivation of recursive formulas based on least squares estimation theory is given. Simulation experiments of this study indicate its validity for on-line parameter tracking applications. Practical considerations in implementing the proposed adaptive estimation system and its extensions to higher-order models are discussed.     

Investigation of heat transfer coefficient in two‐dimensional transient inverse heat conduction problems using the hybrid inverse scheme

A hybrid scheme of the Laplace transform, finite difference and least‐squares methods in conjunction with a sequential‐in‐time concept, cubic spline and temperature measurements is applied to predict the heat transfer coefficient distribution on a boundary surface in two‐dimensional transient inverse heat conduction problems. In this study, the functional form of the heat transfer coefficient is unknown a priori. The whole spatial domain of the unknown heat transfer coefficient is divided into several analysis sub‐intervals. Later, a series of connected cubic polynomial function in space and a linear function in time can be applied to estimate the unknown surface conditions. Due to the application of the Laplace transform, the unknown heat transfer coefficient can be estimated from a specific time. In order to evidence the accuracy of the present inverse scheme, comparisons among the present estimates, previous results and exact solution are made. The results show that the present inverse scheme not only can reduce the number of the measurement locations but also can increase the accuracy of the estimated results. Good estimation on the heat transfer coefficient can be obtained from the knowledge of the transient temperature recordings even in the case with measurement errors. Copyright © 2007 John Wiley & Sons, Ltd.     

Determination of fatty acid profile in cow's milk using mid-infrared spectrometry: Interest of applying a variable selection by genetic algorithms before a PLS regression

The new challenges of the dairy industry require an accurate estimation of fine milk composition. The mid-infrared (MIR) spectrometry method appears to be a good, fast and cheap method for assessing milk fatty acid profile. Although partial least squares (PLS) regression is a very useful and powerful method to determine fine milk composition from the spectra, the estimations are not always very accurate and stable over time. Therefore a genetic algorithm (GA) combined with a PLS regression was used to produce models with a reduced number of wavelengths and a better accuracy. The results are a little sensitive to the choice of parameters in the algorithm. The number of wavelengths to consider is reduced substantially by 4 and accuracy is increased on average by 15%.     

Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures

The problem considered is the identification of two unknown chemical compounds and the estimation of their proportions in a set of unknown mixtures of the two compounds, given data that are vectors of measurements on their mixtures. It is assumed that the expected value of a mixture vector is an unknown convex linear combination of two unknown component vectors and least squares estimation is used to obtain a set of possible solutions of the mixing proportions and the component vectors. Obtaining a unique solution requires additional constraints or information. The solution set is interpreted geometrically and examples involving amino acids and light absorbance data are given.     

光谱Neugebauer模型的抗差最小二乘优化

Yule-Nielsen修正光谱Neugebauer模型是一种用来预测彩色网目调印刷品颜色的重要光谱预测模型。为了提高Neugebauer模型预测精度,在分析光谱Neugebauer模型和抗差估计理论的基础上,提出了将抗差最小二乘法用于计算模型参数网点面积率和基色光谱反射率。常用的抗差估计方案有:Huber估计和IGG估计。实验表明,当存在粗差的情况下,与传统的最小二乘法相比,抗差最小二乘法的光谱Neugebauer模型的预测精度更高且更为稳定。