两个多重相关变量组的统计分析(3)(偏最小二乘回归与PLS过程)

本文用PLS过程建立多因变量的偏最小二乘回归模型 ,并用具体例子对最小二乘回归(MLR)、主成分回归 (PCK)和偏最小二乘回归 (PLS)进行比较     

偏最小二乘回归分析在均匀设计试验建模分析中的应用

本文分析了目前应用一般的最小二乘法建立均匀试验数据的二次多项式回归模型时存在的局限性,提出了应用偏最小二乘法(Partial least-square,PLS)建立二次多项式回归模型的技术,并且进一步介绍了偏最小二乘回归(PLS回归)在均匀设计中的应用。作者认为,PLS回归分析建模技术将为均匀设计的更广泛应用提供有力的技术支持。     

偏最小二乘回归在选矿效益建模中的应用

选矿效益对矿管理有着重要意义。影响选矿效益的因素之间存在严重的多重共线性,采用PLS方法建立了选矿效益的偏最小二乘回归模型,避免了普通多元回归模型的不合理性和岭回归模型选择岭参数的主观性。     

偏最小二乘回归法在武器装备研制费用估算中的应用

参数估算法作为 LCC的一种估算方法主要应用于武器装备研制费用的估算 .由于样本数据较少 ,且变量之间的线性相关程度高 ,如果使用传统的普通最小二乘法 (OLS)估算 ,则会严重降低估计结果的有效性 .而偏最小二乘回归法 (PLS)可以克服样本点少和高线性相关性的问题 ,使估算结果更趋于真值 .以某型无人侦察机的研制费用估算和美国军用飞机发动机研制费用估算为例 ,主要研究偏最小二乘回归法 (PLS)在武器装备研制费用估算中的应用     

一类小样本的统计方法建模及其可视化

针对一类高维小样本数据,利用统计方法的非参数检验与偏最小二乘回归(PLS)构造小样本预测模型,实现基于Wilcoxon秩和检验的变量选择与基于PLS的变量压缩降维.并通过DNA序列分类问题实现基于统计方法的小样本数据建模与可视化,计算结果表明方法对小样本具有可行性、有效性.     

偏最小二乘回归方法(PLS)在短期气候预测中的应用

对广西88个站冬季(12月、1月和2月)各月平均气温距平场作自然正交展开(EOF分解),选取累积方差贡献超过90%的前3个主成分作为预报量.从前期平均大气环流场和海温场中查找预报因子,对这些初选因子用偏最小二乘回归方法(PLS)进行信息筛选和成分提取,用提取的新综合变量(又称成分)作预报因子,分别建立各月平均气温前3个主成分的回归预报方程.经独立样本预报试验证明,偏最小二乘回归方法具备良好的因子信息提取能力,其预报建模方法对冬季月平均气温预报具有较好的预测效果.     

模糊线性回归模型的约束最小二乘估计

自Tanaka等1982年提出模糊回归概念以来,该问题已得到广泛的研究。作为主要估计方法之一的模糊最小二乘估计以其与统计最小二乘估计的密切联系更受到人们的重视。本文依据适当定义的两个模糊数之间的距离,提出了模糊线性回归模型的一个约束最小二乘估计方法,该方法不仅能使估计的模糊参数的宽度具有非负性而且估计的模糊参数的中心线与传统的最小二乘估计相一致。最后,通过数值例子说明了所提方法的具体应用。     

偏最小二乘回归方法的局限性及改进算法

提出了偏最小二乘回归中的一类不适用情况,并从理论上分析,实例上验证,给出了针对这种情况的一种改进算法,从而拓宽了偏最小二乘回归的使用范围.     

剔除相关性的最小二乘研究

本文提出了一种新的回归模型,剔除相关性的最小二乘,它有效的克服了变量间的相关性,兼顾到变量的筛选。并与最小二乘、向后删除变量法、偏最小二乘比较分析。发现剔除相关性的最小二乘能很好的处理自变量间多重相关性,对变量进行有效的筛选,克服了回归系数反常的现象。     

基于灰色关联分析与PLS-LSSVM的航材备件需求预测模型

航材备件是保障航空装备日常训练和作战正常使用的重要影响因素,针对部分航材备件样本数据量少,影响因素多且复杂多变,预测结果与装备系统完好性要求偏差较大等问题.建立基于灰色关联分析(GRA)与偏最小二乘(PLS)及最小二乘向量机(LSSVM)相结合的航材备件预测模型,采集某无人机航材备件数据,通过对统计数据进行灰色关联分析...     

碾压混凝土坝施工层面变形分析模型

针对碾压混凝土坝施工层面对大坝变形产生显著影响的问题,深入研究了施工层面的变化性质及规律,提出了层面不同阶段变形的模拟方法,建立了施工层面有厚度和无厚度分析模型,提出的模型能反映层面的弹性变形、衰减蠕变、不可逆变形以及加速蠕变等变形状态．实例分析表明:所提出的碾压混凝土坝施工层面有厚度和无厚度分析模型能较客观地模拟大坝的结构变化形态,尤其是施工层面有厚度分析模型较完整地模拟了层面的渐变规律,其计算结果与原位监测成果吻合较好．同时,提出的方法和建立的分析模型可推广应用于常规混凝土坝,特别是坝基内断层和夹层等变形规律的分析．     

一类柔性臂机器人的稳定性

本文研究了一类柔性臂机器人的控制问题,且柔性臂的弯曲振动与扭转振动的耦合作用表现在边界方程中。本文运用算子谱理论、算子半群理论等,得到系统的主算子生成的C0-半群的具体表示式,并证明了半群的解析性、非紧性及非一致指数稳定性。     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

Variational analysis of functions of the roots of polynomials

The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the roots, we obtain characterizations of the subderivative and regular subdifferential for these functions as well. In particular, we completely characterize the subderivative and regular subdifferential of the radius mapping (the maximum of the moduli of the roots). The abscissa and radius mappings are important for the study of continuous and discrete time linear dynamical systems. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday. Terry is one of those rare individuals who combine a broad vision, deep insight, and the outstanding writing and lecturing skills crucial for engaging others in his subject. With these qualities he has won universal respect as a founding father of our discipline. We, and the broader mathematical community, owe Terry a great deal. But most of all we are personally thankful to Terry for his friendship and guidance. Research supported in part by the National Science Foundation Grant DMS-0203175. Research supported in part by the Natural Sciences and Engineering Research Council of Canada. Research supported in part by the National Science Foundation Grant DMS-0412049.     

白骨化尸体死亡时间的推断

本文分析了15具白骨化尸体标本的股骨汞(Hg),铅(Pb),镉(Cd)元素含量数据,在三年的时间内采集了3次,一共收集到45个数据。首先将这组数据看着纵向数据,利用线性随机效应混合模型、Cox随机混合效应模型进行分析,结果显示,如果对每个白骨化尸体标本建立线性模型,可以精确预测出死亡时间,而且不需要采集铅元素含量数据。混合效应模型的预测效果也很好,最大误差不会超过1个月。其次我们对数据不作任何假设,利用机器学习中随机森林方法分析数据,并利用5折交叉验证方法来判断结果的可靠性,训练集和测试集的NMSE分别为0.1205944,0.5604286,因此可以用训练出的模型来预测死亡时间。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Modelling and analysis of dynamics of viral infection of cells and of interferon resistance

Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.     

Analytic description of statistics of spectra of quantum graphs

We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.