不等式约束条件下回归模型的参数估计及检验

本文研究了具有不等式约束条件的回归模型的参数估计，给出了检验的统计量和一个实例．     

误差非线性回归模型基于几何方法的若干二阶渐近性质

该文用微分几何方法对AR(q)误差非线性回归模型若干二 阶渐近性质进行了研究. 作者基于Fisher信息阵在欧氏空间定义了内积，并在期望参数空间建立了几何结构. 基于上述几何结构，给出了AR(q)误差非线性回归模型若干二阶渐近性质的曲率表示. 将前人的一些结果推广到AR(q)误差非线性回归模型.      

带优化参数的SVR模型及在软件成本估算中的应用

随着社会各行各业对软件开发投资的日益增长,产业界和学术界越来越关注可靠的软件成本估算,以有效控制软件开发过程中相关风险.为了能更准确地估算软件成本,提出一种带遗传算法优化参数的支持向量回归机模型,用遗传算法来优化支持向量回归机模型中的参数集(C,γ,ε),可以避免参数选择的盲目性,能显著提高支持向量回归机模型的预测能力.分别用IBM DP、Kemerer和Hallmark三个数据库来验证模型的有效性,并与常用的线性回归模型进行对比,结果显示采用遗传算法优化的支持向量回归机模型具有很好的学习精度和推广能力,在MMRE和Pred(0.25)两个标准上都优于线性回归模型.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Adaptive nonparametric estimation of a multivariate regression function

We consider the kernel estimation of a multivariate regression function at a point. Theoretical choices of the bandwidth are possible for attaining minimum mean squared error or for local scaling, in the sense of asymptotic distribution. However, these choices are not available in practice. We follow the approach of Krieger and Pickands (Ann. Statist.9 (1981) 1066–1078) and Abramson (J. Multivariate Anal.12 (1982), 562–567) in constructing adaptive estimates after demonstrating the weak convergence of some error process. As consequences, efficient data-driven consistent estimation is feasible, and data-driven local scaling is also feasible. In the latter instance, nearest-neighbor-type estimates and variance-stabilizing estimates are obtained as special cases.     

Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

双层PLS算法及其在近红外光谱分析中的应用

针对近红外光谱数据局部效应显著,变量个数多,且彼此间常存在严重的复共线性,并与样品组分含量呈非线性关系,构建了一种双层非线性偏最小二乘回归 (DNPLSR)算法。它将非线性回归和偏最小二 乘(PLS)相结合,先在外层由PLS从样本数据中提取成分,并实现每对成分间的非线性映射,再在内层实施PLS算法,将外层因变量成分的拟合误差反馈计算转换权向量的增量,进一步修正转换权向量,以使外层所提取的成分对因变量具有更优的解释能力。最后,将该法应用于80个谷物样品的水组分含量与其近红外光谱的定量关系建模,效果良好,显示出很强的学习能力,所建模型的预报性能也优于其他方法。     

光程对黄酒金属元素近红外透射光谱分析精度的影响

应用近红外透射光谱分析技术开展了不同光程对黄酒中金属元素(钾、钙、镁、锌和铁)分析结果影响的研究。实验采用傅里叶变换近红外光谱仪(800～2 500 nm)及不同光程(1,2,5,10 mm),石英比色皿以空气为参比进行了光谱采集,并采用偏最小二乘法进行了数据分析。金属含量采用原子吸收光谱分析法测定。分析结果表明, 5 mm光程的分析结果最优,对于钾、钙、镁、锌和铁的相关系数(r2)分别为0.93,0.85,0.93,0.72,0.66,交互验证误差(RMSECV)分别为26.5,35.6,4.63,0.26,0.64 mg·L-1;而10 mm光程的光谱分析结果最差,其r2分别为0.61,0.65,0.63,0.09,0.25。通过实验说明, 光程对近红外透射光谱分析的影响,不是光程越长或越短越好,需要通过测试及对比分析确定。     

油菜叶片的光谱特征与叶绿素含量之间的关系研究

叶绿素是作物生长中的重要因素,是植物营养胁迫、光合作用能力和生长状况的良好指示剂。实时、可靠的作物营养诊断是进行科学施肥管理的基础,也是实践精细农业的关键技术之一。采用便携式可见-近红外光谱仪,在室外自然光照条件下对不同氮肥水平下油菜叶片的光谱特性进行了研究,并根据作物特有的光谱特征,采用逐步回归分析方法建立了油菜叶片的叶绿素含量与红边位置和绿峰位置之间的定量分析模型。结果表明,将红边位置、绿峰位置二者作为自变量时,建立的模型效果优于采用单一的红边位置为自变量时建立的模型效果。其相关系数分别为0.863和0.848;校正标准偏差SEC分别为5.273和5.459, 说明采用红边位置和绿峰位置这两个参数更能很好地预测叶片的叶绿素含量。