消除复共线性影响的一种新的解决办法

基于响应变量和解释变量的数据中都含有观测误差这一新的认识．将设计矩阵中有复共线性的多元线性回归模型修正为一种多元线性Errorg—in—variables模型，从而尽量消除复共线性的影响，得到较好的回归系数估计，文中给出了两个模拟倒子，表明了用此修正模型所得的估计结果非常接近参数真值．从前说明提出的方法是一种很有效的消除复共线性影响的方法。     

多元线性模型回归系数的主成分估计

本文对多元线性模型回归系数提出了主成分估计，并证明了主成分估计优于最小二乘估计。进一步，对最小二乘估计的任一线性变换，给出了均方误差的一个无偏估计，并应用极小化均方误差的无偏估计的方法，给出了确定偏参数的公式。     

线性回归模型系数Stein估计的改进研究

针对线性回归模型病态的根本原因，提出了一类新的估计——c-k型估计，将岭估计与Stein估计统一到一个估计类；研究了这一估计类，证明利用岭回归技术可以改进著名的Stein估计(在均方误差意义下)；同时研究了相应参数的最优值，分别给出了它的一个上界及下界，为病态线性回归模型系数的有偏估计提供了改进的技术途径．     

多元约束Welsch-Kuh距离与多元约束Cook距离

对多元约束线性回归模型，本文讨论了约束最小二乘估计的影响问题，定义了度量影响的多元约束Ｃｏｏｋ距离和多元约束Ｗ－Ｋ统计量，给出了其分布，建立了约束Ｗ－Ｋ统计量与约束广义相关系数之间的联系。     

多元线性正态SRM参数估计的渐近协方差阵及其估计

针对多元线性正态结构关系模型（SRM）,本文给出了真值向量协方差阵的广义逆构造,并在三种常见误差协方差阵假定下应用标准5法分别给出了模型结构参数约束最小二乘估计的渐近协方差阵及其相合估计。     

半参数单调回归EV模型的估计

半参数回归模型在工程、经济和医学问题中有着广泛的应用,但是实际问题中数据往往带有测量误差,并且许多情况下解释变量和某些响应变量之间的关系是单调的,此时普通的参数最小二乘估计是有偏的,且非参数部分的估计无法保证单调性.本文针对这两个问题研究了半参数单调回归模型,得到了参数的无偏估计,同时非参数部分估计具有单调性,并得到了...     

基于复相关系数的时滞联合估计及其应用

针对工业过程的软测量建模,为对输入与输出变量间的时滞关系进行准确、快速地估计,提出一种基于复相关系数的时滞联合估计方法。该方法以模型输入和输出数据间的复相关系数为指标,将时滞联合估计问题转化为多维优化问题,进而对各输入变量的时滞时间进行寻优。针对火电厂脱硝系统的NO_x排放软测量,基于实际的运行数据和最小二乘支持向量机算法,对所提出的方法进行验证并与其他时滞估计方法进行对比。结果表明:基于复相关系数的时滞估计方法计算速度较快,时滞估计结果较准确,能在一定程度上提高软测量模型的准确度。     

顾客满意度线性建模中多重共线性处理方法的模拟研究

多重共线性会给顾客满意度线性建模带来很大的危害。本文综述了四种处理多重共线性的方法,即逐步回归法、岭回归法、主成分回归法和偏最小二乘法,并使用蒙特卡罗方法,对这四种方法在建模可靠性、模型解释能力及模型预测能力方面进行了仿真比较。结果表明,存在多重共线性时,偏最小二乘法的建模效果最为理想。     

基于时延估计的海底线阵阵形估计方法研究

阵形估计是水听器阵列应用中的关键问题,基于时延估计的阵形估计方法比基于传感器测量和基于匹配场处理的方法具有更强的适应性和较高的精度。针对浅海水听器阵列中水平长线阵存在的纵向相关振荡现象引起的不能简单以某一阵元为基准求相对时延的问题,充分利用了阵元信号的高相关性,提出了基于子阵时延的阵形估计方法,针对子阵间时延估计误差向阵端累积的问题,该方法以时延估计的克拉美罗界为依据提出了合理的子阵方式,在一定程度上减小了误差传递。对已有海试数据阵形估计处理的结果表明,相对于单源固定间距方法和未分子阵的双源时延估计方法,基于子阵时延的阵形估计方法满足阵元间距的约束,有较好的空间谱特性,减小了阵形估计误差,对长水听器阵列的应用及阵形估计具有较大应用价值。     

多元线性模型系数的主成分估计及其筛选

在试验统计所涉及线性模型系数 β估计问题中 ,当观测值矩阵存在多重共线性 ,往往会导致通常意义下的回归分析失去实用价值 .此处提供 RMS和 AIC准则确定主成分并对模型中参数作出主成分估计 ,从而较大幅度地降低多重共线性 ,并减少了估计值的均方误差 ,用以改进试验统计中的精度     

Effective Control Charts for Monitoring Multivariate Process Dispersion

When monitoring process dispersion, it is common to pay more attention to dispersion increases than to decreases for practical reasons. Nonetheless, it is also important to detect dispersion decreases for two reasons: (i) it deserves further investigations as to why the process has improved; and (ii) if the process has changed, the settings of the control chart would need to be adjusted for effective future monitoring. In this paper, we first propose an effective control chart for detecting multivariate dispersion decreases in phase II process monitoring, which is constructed using the same approach as that of the one‐sided likelihood‐ratio‐test‐based multivariate chart proposed recently in the literature for detecting dispersion increases. We then discuss a combined charting scheme by combining these two one‐sided charts for detecting either dispersion increases or decreases. Comparative simulation studies show that the proposed combined control charting scheme outperforms several existing two‐sided control charts in terms of the average run length when the process dispersion indeed increases or decreases. Two real‐life examples are presented to demonstrate the applicability of the proposed charts. Copyright © 2011 John Wiley & Sons, Ltd.     

Bayes Linear Estimators

A class of linear estimators, called Bayes linear estimators, is developed by finding, among all linear estimators, ones which have least average total mean squared error, averaged over parameter points. Ridge, generalized ridge, restricted least squares, subset least squares, least squares, best, and generalized inverse linear estimators are all either Bayes linear estimators or limits of Bayes linear estimators. Results on Bayes linear estimators are extended to affine estimators. “Bootstrapping” procedures, in which the data are recycled in the guise of prior information, are discussed.     

Discussion

The use of Stein estimation in multiple linear regression is considered. Tables and graphs are presented that compare the prediction mean squared errors of positive-part James-Stein, preliminary-test, reduced, and full-model least squares estimates. The appropriateness of using Stein contraction on possibly extraneous variables is emphasized, and a procedure is presented for evaluating the likely savings in using Stein estimation on the problem at hand. An example is given.     

Estimation of the variance for a controlled branching process

In this paper we obtain estimators for the variance of the offspring distribution of a controlled branching process and we derive, for these estimators, some moments and asymptotic properties as consistency and limiting distribution. Research supported by the Ministerio de Ciencia y Tecnología and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2003-06074.     

Nonparametric estimation of the offspring distribution and the mean for a controlled branching process

In this paper, under a nonparametric context, some estimators for the mean and the offspring distribution of a controlled branching process are provided. Their conditional and unconditional moments and their asymptotic properties (consistency, normality) are investigated. Finally, as an illustration, a simulated example is presented. Research supported by the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2000-0356 and the Consejería de Educación, Ciencia y Tecnología de la Junta de Extremaduray y el Fondo Social Europeo, grant IPR00A056.     

Proceedings of the Computer Science and Statistics: 12th Annual Symposium on the Interface

This article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution, leave-one-out, and bootstrap estimators. Smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing. An algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector. Using the criterion of unconditional mean squared error, this particular smoothed estimator, called the NS method, appears to offer a reasonable alternative to existing nonparametric estimators.     

A General Simulation Programme for Material Flow in Batch Chemical Plants

Techniques for the simulation of material flow through multi-stage full-scale batch chemical plants are described and the need for general computer programmes is argued. An outline is given of a general simulation programme written in ‘Mercury’ auto-code, which is based on the reduction of interstage pipe networks to a small number of “common mains.”     

Process monitoring in real time: Empirical bayes approach—discrete case

In this paper an empirical Bayes model is developed to monitor and analyse discrete data generated in a manufacturing process for printed circuit boards. A key feature of this analysis is the use of the current observation at time t and the posterior estimates of the distribution of the proportion nonconforming at time t – 1 to obtain a new, updated estimate of the posterior distribution at time t. The derived approach is widely applicable to statistical process control and provides a simple and fast algorithm for updating.     

On properties of probability-based multivariate process capability indices

Multivariate process capability indices (MPCIs) have been proposed to measure multivariate process capability in real-world application over the past three decades. For the practitioner's point of view, the intention of this paper is to examine the performances and distributional properties of probability-based MPCIs. Considering issues of construction of capability indices in multivariate setup and computation with performance, we found that probability-based MPCIs are a proper generalization of univariate basic process capability indices (PCIs). In the beginning of this decade, computation of probability-based indices was a difficult and time-consuming task, but in the computer age statistics, computation of probability-based MPCIs is simple and quick. Recent work on the performance of MPCI NMC_pm and distributional properties of its estimator reasonably recommended this index, for use in practical situations. To study distributional properties of natural estimators of probability-based MPCIs and recommended index estimator, we conducted simulation study. Though natural estimators of probability-based indices are negatively biased, they are better with respect to mean, relative bias, mean square error. Probability-based MPCI MC_pm is better as compared with NMC_pm with respect to performance and as its estimator quality. Hence, in real-world practice, we recommend probability-based MPCIs as a multivariate analogue of basic PCIs.     

An MSE comparison of the restricted Stein-rule and minimum mean squared error estimators in regression

In this paper, we consider the feasible minimum mean squared error (FMMSE) estimator and the adjusted FMMSE (AFMMSE) estimator which are obtained by shrinking the ordinary least squares (OLS) estimator towards the restricted least squares estimator. We derive the formulas of MSE for the restricted FMMSE and AFMMSE estimators. By numerical evaluations, the MSE performances of the restricted FMMSE and AFMMSE estimators are compared with that of the restricted positive-part Stein-rule estimator.