The robustness and efficiency of trimmed elemental estimation in regression analysis: a Monte Carlo simulation study

Mayo and Gray [Am Statist 51 (1997) 122] introduced the leverage-residual weighted elemental (LRWE) classification of regression estimators and proposed a new method of estimation called trimmed elemental estimation (TEE). In this article, we perform a simulation study of the efficiency of certain TEE estimators relative to ordinary least squares under normal errors and their robustness under various non-normal error distributions in the context of the simple linear regression model. Comparisons among these estimators are made on the basis of mean square error and percentiles of the absolute estimation errors in the simulations.     

异方差随机系数回归模型的最优设计

最优设计方法在工程技术领域和工农业生产中具有广泛的应用．随机系数模型的最优设计研究中通常假定随机误差项具有相同的方差,实际中误差的产生往往与观测点有关,从而具有异方差性质．本文研究一般闭区间设计域上异方差随机系数回归模型的最优近似设计问题．我们获得了最优设计可以在设计域的两个端点处得到的一组充分条件,并进一步证明了当误差项方差具有对称结构且设计域是对称区间时,设计域两个对称端点处的等权重设计同时具有多重最优性质,这时最优设计不依赖于模型中随机误差项的方差结构及随机系数项的方差．     

球笼式等速万向联轴器强度设计缺陷的回归辨识

复杂机械产品零部件的强度受多因素影响,且这些影响因素与零部件强度之间的关系非常复杂,常常难以建立其解析的数学模型,这给复杂机械产品零部件强度设计缺陷的辨识带来了困难．以球笼式等速万向联轴器为研究对象,将其内外沟道的接触应力作为强度判断的依据,将历史设计方案中影响零部件接触应力的设计参数作为因变量,建立接触应力与各相关影响因素的回归方程,通过拟合后的回归方程分析各因素对内外沟道强度的影响程度,计算出各影响因素的最大拟合误差值．将新设计方案中影响零部件接触应力的设计参数代入回归方程,求得参数设计值与回归方程的输出值之间的差值,将此差值与回归方程最大拟合误差值进行对比分析,辨识出球笼式等速万向联轴器设计中存在的强度设计缺陷,有效提高了设计质量和效率．     

ESVR算法及支撑向量机算法中参数的确定

支撑向量机是基于有限数据的机器学习算法,主要研究如何从一些给定的观测数据获得目前尚不能通过原理分析得出的规律,利用这些规律去分析客观现象并对无法观测的数据进行预测。本文在已有的支撑向量机算法的基础上,提出了一种新的算法——ESVR算法,它是基于支撑向量回归机的改进算法,利用原有用于回归问题的SVM算法消除了孤立点对已知问题的影响。针对支撑向量机算法中核参数取值对推广性的影响较明显的特点,本文给出了一种核函数中参数的确定方法——渐进搜索法,它可以得到支撑向量机算法中核参数的取值范围,并具有推广误差较小的特点。数值实验表明它们具有较好的效果。     

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.     

半参数回归模型拟极大似然估计的弱相合性

本文考虑一类固定设计的半参数回归模型,其误差为一阶自回归时间序列。用权函数及拟极大似然估计方法得到了一些参数及非参数的拟极大似然估计量,在适当的条件下,研究了它们的弱相合性,从而丰富了该类半参数回归模型的估计理论与方法。     

Analysis of algorithmic errors and mistakes in regression treatment of geomagnetic measurements

Algorithms are considered for localization of epicentral zones of pulse geomagnetic sources. A procedure is proposed for overcoming errors and increasing the accuracy of processing geomagnetic data on the basis of regression treatment of wave packages. __________ Translated from Metrologiya, No. 11. pp. 18–27, November, 2007.     

Diagnostics for Nonlinearity and Heteroscedasticity in Errors-in-Variables Regression

We suggest new plotting methods for residual analysis in errors-in-variables regression. The standard residuals analyses are based on the methods of Miller and Fuller and are appropriate when the errors in the regression and the measurement error are symmetrically distributed. By “appropriate,” we mean that in large samples the plots will not falsely identify a nonexistent pattern of heteroscedasticity or nonlinearity. The standard methods are not appropriate in this sense for skewed error distributions. Our methods require replication of the error-prone predictors, but they are appropriate for both symmetric and skewed error distributions. Besides residual plots, we also construct hypothesis tests for heteroscedasticity. In terms of power for detecting heteroscedasticity, we show that the standard plot is more efficient when the residuals are normally distributed, although it does not achieve its nominal level for skewed error distributions. Simulations are used to illustrate the results. We also consider the case that measurement error in the response is correlated with the measurement error in the predictors, suggesting new residual plots in this setting. The article also contains a short summary of plotting techniques for detecting heteroscedasticity in regression.     

汽车噪声限值预测模型与分析

汽车噪声是道路交通噪声的重要组成部分,直接影响城市道路交通声环境质量和居民日常生活,持续降低有关汽车噪声法规中汽车噪声限值有利于提高道路交通声环境质量.对某汽车噪声法规及其限值进行分析,采用最小二乘法建立汽车加速行驶时车外噪声限值的线性回归、二次回归预测模型,得到噪声限值预测值.从预测模型分析结果可知:二次回归预测模型...     

基于GWO的SVM在红外甲烷传感器测量误差分析中的应用

针对传统支持向量机回归模型应用在红外甲烷传感器测量数据处理时出现预测精度低的问题,提出了一种基于灰狼优化算法的支持向量机回归模型。该模型在传统支持向量机的基础上,利用灰狼优化算法自适应搜索特征空间来选择最佳特征组合,经过循环比较,能快速、准确地搜索到最优的惩罚因子C与gamma参数。用实验室研制的红外甲烷传感器对0～5.05%浓度范围的标准甲烷气体进行测量后,建立了3种SVM回归模型,并进行对比。结果表明,采用灰狼优化算法建立的支持向量机回归模型其绝对误差和相对误差小,精度高。     

Multiresponse Models for Calibrating Scanners

A method of calibrating scanners based on multiresponse regression models which connect the color parameters of color images of a calibrated light target with the results of the scanning of this target is proposed. A procedure and the results of an analysis of the covariance matrices of the errors of observation of the color parameters for different types of scanners are presented. Estimates of the prediction capability of the proposed calibration method are given and comparative results of its use are presented.     

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。     

Impact of gender, age and experience of pilots on general aviation accidents

General aviation (GA) accounts for more than 82% of all air transport-related accidents and air transport-related fatalities in the U.S. In this study, we conduct a series of statistical analyses to investigate the significance of a pilot's gender, age and experience in influencing the risk for pilot errors and fatalities in GA accidents. There is no evidence from the Chi-square tests and logistic regression models that support the likelihood of an accident caused by pilot error to be related to pilot gender. However, evidence is found that male pilots, those older than 60 years of age, and with more experience, are more likely to be involved in a fatal accident.     

广义距离回归

实际工作中涉及的两个测得量的回归极为有用.从一个量有不确定度的一般回归讨论到两个量有不确定度的正交回归,最后讨论到普遍的广义距离回归,并以实例说明.     

A two-stage regression approach for spectroscopic quantitative analysis

In this paper, we propose a two-stage regression approach, which is based on the residual correction concept. Its underlying idea is to correct any given regressor by analyzing and modeling its residual errors in the input space. We report and discuss results of experiments conducted on three different datasets in infrared spectroscopy and designed in such a way to test the proposed approach by: 1) varying the kind of adopted regression method used to approximate the chemical parameter of interest. Partial least squares regression (PLSR), support vector machines (SVM) and radial basis function neural network (RBF) methods are considered; 2) adopting or not a feature selection strategy to reduce the dimension of the space where to perform the regression task. A comparative study with another approach which exploits differently estimation errors, namely adaptive boosting for regression (AdaBoost.R), is also included. The obtained results point out that the residual-based correction approach (RBC) can improve the accuracy of the estimation process. Not all the improvements are statistically significant but, at the same time, no case of accuracy decrease has been observed.     

基于灰色回归模型广州市果蔬类生鲜农产品冷链物流需求预测

目的 通过对不同预测方法的误差进行对比研究,选取预测精度较高的方法,促进部门科学化决策。方法 从农产品供给、社会经济水平、冷链物流保障、居民规模与消费能力四大维度选取15个指标来构建影响因素指标体系,对影响因素与冷链物流需求进行灰色关联度分析。采用GM(1,1)、GM(1,6)与主成分-多元回归线性模型对果蔬类生鲜农产品冷链物流需求进行预测。结果 GM(1,1)预测模型、GM(1,6)预测模型、主成分-多元回归线性预测模型的预测误差分别为2.97%、1.70%、2.53%。结论 GM(1,6)预测模型预测精度最高,该模型适用于中短期的冷链物流需求预测,具有较高的应用价值。     

Cluster‐Based Bounded Influence Regression

A regression methodology is introduced that obtains competitive, robust, efficient, high‐breakdown regression parameter estimates as well as providing an informative summary regarding possible multiple outlier structure. The proposed method blends a cluster analysis phase with a controlled bounded influence (BI) regression phase, thereby referred to as cluster‐based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point‐addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster ‘half‐set’ of observations, with the remaining observations comprising one or more minor clusters. An initial regression estimator arises from the main cluster, with a group‐additive DFFITS argument used to carefully activate the minor clusters through a BI regression frame work. CBI achieves a 50% breakdown point, is regression equivariant, scale and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo results demonstrate the performance advantage of CBI over other popular robust regression procedures regarding coefficient stability, scale estimation and standard errors. The dendrogram of the clustering process and the weight plot are graphical displays available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical view point towards data analysis and the marriage of estimation with diagnostic summary. Copyright © 2013 John Wiley & Sons, Ltd.     

锅炉炉膛热负荷分布拟合算法研究

锅炉炉膛辐射热负荷测量及分布规律的研究可为蒸发受热面及节流孔设计提供必需的数据。提出了炉 膛热负荷测量数据的处理方法,将测得的热负荷数据转换成相对于蒸发受热面平均热负荷的分配不均系数,该系数是炉膛相对高度的函数,它的多项式回归模型不仅要使误差平方和达到最小,而且根据平均热负荷的定义,多项 式系数还要满足给定的等式约束。对于采用普通燃烧技术和空气分级燃烧技术的两类燃煤锅炉,利用该回归模型拟合炉膛辐射热负荷数据,得到不同的分布规律,并与某300 MW锅炉炉膛热负荷测量数据进行了对比;这种以最 小二乘法为基础的改进回归模型既满足了回归变量的内在联系,又对测量数据进行了最佳逼近。     

Model complexity versus scatter in fatigue

Fatigue assessment in industry is often based on simple empirical models, such as the Wöhler curve or the Paris' law. In contrast, fatigue research to a great extent works with very complex models, far from the engineering practice. One explanation for this discrepancy is that the scatter in service fatigue obscures many of the subtle phenomena that can be studied in a laboratory. Here we use a statistical theory for stepwise regression to investigate the role of scatter in the choice of model complexity in fatigue. The results suggest that the amount of complexity used in different design concepts reflects the appreciated knowledge about input parameters. The analysis also points out that even qualitative knowledge about the neglected complexity may be important in order to avoid systematic errors.     

Insights into isotherm making in the sorptive removal of fluoride from drinking water

The defluoridation research has thrown up many technologies, with adsorption as a popular alternative, especially among fluoride endemic habitations of the developing world. In the endeavor to develop novel adsorbents for defluoridation, the adsorption potential of hardened alumina cement granules (ALC) were examined through isotherm fitting. Though the adsorbent showed enhanced adsorption capacity at higher fluoride concentration ranges, the errors associated with linearization in isotherm fitting were also found to be increasing. The propagation of these errors was more prominent in Dubinin-Radushkevich and Langmuir models but negligible in Freundlich. The chi2 analysis, used to correlate the equilibrium experimental data and the isotherm models, also suggested poor correlations at higher fluoride concentration ranges for all the models. The procedure of linear and nonlinear regression through optimization of error functions rendered the 'best-fit' model and optimum model parameters, through sum of normalized error (SNE) values. Though ALC exhibited maximum monolayer adsorption capacity of 34.36 mgg(-1) in concentration variation studies of fluoride in the range of 2.5-100 mg l(-1) in synthetic water, it got reduced to 10.215 mgg(-1) in dose variation studies and further to 0.9358 mgg(-1) in natural ground water. Though Langmuir appeared as the best-fit model in terms of R2 in synthetic studies of different fluoride concentrations, the procedure of linear and nonlinear regression demonstrated that Freundlich was the best-fit. The nonlinear chi2 analysis together with minimum SNE values convincingly demonstrated that the equilibrium studies with dose variations of ALC offers more reliable isotherm parameters than those with high fluoride concentrations. The sorption of fluoride by ALC appeared endothermic with Freundlich adsorption capacity parameter increased from 0.5589 to 0.9939 lg(-1) in natural water and 3.980-7.5198 lg(-1) in synthetic water systems for a rise in temperature from 290 to 310 K. The study deviates from conventional methodologies of relying solely on R2 values in selecting 'best-fit' isotherm model, and basically demonstrates how the optimum model parameters like 'adsorption capacity' evolves through linear and nonlinear regression using error functions.