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。     

带约束的增长曲线模型中回归系数线性估计的可容许性

在两种矩阵损失函数下讨论了带约束的增长曲线模型中回归系数线性估计的可容许性,并在齐次线性估计类和非齐次线性估计类中得到了容许性的充要条件.     

局部线性回归模型的半参估计

针对局部线性估计方法收敛速度较慢且对窗宽选择不稳健的问题,本文提出一种改进的局部线性半参估计方法。首先,选择不同窗宽作相应的局部线性估计,然后利用这些估计构造参数回归模型,由此给出回归函数的参数估计。相对于局部线性估计,新方法在不改变方差阶的情况下,将估计偏差的阶由h2减小至h4,最优均方收敛速度提高至O(n?89),且对窗宽选择稳健。模拟研究验证了新方法的有效性。     

线性不适定问题中选取Tikhonov正则化参数的线性模型函数方法

如何选取正则化参数是不适定问题Tikhonov正则化的一个重要问题。基于吸收的Morozov偏差原理,研究了正则化参数选取的线性模型函数方法。在从Hermite插值角度导出线性模型函数后,讨论了选取正则化参数的两种线性模型函数算法(基本算法与改进算法)及其收敛性。为克服基本算法的局部收敛性,提出了一种新的线性模型函数松弛算法。并且,提出了两种具有全局收敛性的组合算法,即线性与线性模型函数算法、双曲型与线性模型函数算法。数值实验说明了所提算法的有效性。     

线性乘性规划的全局优化算法

本文研究线性乘性规划问题(LMP)的全局最优化算法,线性乘性规划问题在生产运输、工厂布局设计、超大规模集成电路芯片设计等方面有重要的应用。首先将LMP问题转化为等价规划问题(P1),然后利用参数线性化方法在相应的超矩形上求得问题(P1)的目标函数和约束函数线性下界估计,并提出了一个求线性乘性规划全局解的确定性全局优化算法,并证明了算法的收敛性。数值实验表明提出的方法是可行和有效的。     

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.     

部分变量带误差的线性函数关系模型的参数估计及相合性

本文讨论了部分变量带误差的线性函数关系模型的参数估计问题，在较弱条件下证明了所获得的估计的强相合性，并给出了收敛速度。     

高阶线性微分方程的复振荡性质

研究了亚纯函数系数的高阶齐次线性微分方程的复振荡，得到了解的超级和超级零点收敛指数的估计。     

一阶拟线性双曲型方程组Goursat问题经典解的破裂机制(英文)

对一阶拟线性双曲型方程组的Goursat问题,利用特征线方法及波分解公式,在方程组不是弱线性退化的假设下,当特征边界上给出的边界函数C1范数充分小、且满足一定衰减性时,得到其C1解的破裂机制及关于生命跨度的渐近估计.     

带线性不等式约束的线性模型中线性预测的可容许性

本文刻画了线性模型在线性不等式约束条件下的线性预测的可容许性。我们给出了条件线性可预测变量和线性不等式约束条件下可容许预测的定义,在二次损失函数下,讨论了齐次和非齐次线性预测可容许性的关系,得到了条件线性可预测变量的线性预测是可容许线性预测的充要条件。     

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 of the Papers of Messrs. Satterthwaite and Budne

This article considers minimax linear estimation of β in the multiple linear-regression model Y = Xβ + ξ. Some results from European publications are referenced and summarized and some new results are given. These minimax estimators of β can also be classified as ridgeregression estimators with nonstochastic ridge parameters. Some ridge-regression estimators with stochastic ridge parameters can be motivated by minimax estimation considerations. These minimax-based estimators are discussed and the results ofa simulation study are summarized.     

一般增长曲线模型中随机回归系数线性估计的可容许性

本文在矩阵损失下研究了一般增长曲线模型中随机回归系数线性估计的可容许性。分别在齐次线性估计类和非齐次线性估计类中得到了随机回归系数的一个线性估计是可容许的充要条件。     

Change Point Estimation in the Mean of Multivariate Linear Profiles with No Change Type Assumption via Dynamic Linear Model

Change point estimation is a useful concept that helps quality engineers to effectively search for assignable causes and improve quality of the process or product. In this paper, the maximum likelihood approach is developed to estimate change point in the mean of multivariate linear profiles in Phase II. After the change point, parameters are estimated through filtering and smoothing approaches in dynamic linear model. The proposed change point estimator can be applied without any prior knowledge about the change type against existing estimators which assume change type is known in advance. Besides, sporadic change point can be identified as well. Simulation results show the effectiveness of the proposed estimators to estimate step, drift and monotonic, as well as sporadic changes in small to large shifts. In addition, effect of different values of the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart smoothing coefficient on the performance of the proposed estimator is investigated presenting that the smoothing estimator has more uniform performance. Copyright © 2015 John Wiley & Sons, Ltd.     

部分线性变量含误差的网格数据模型的估计

针对网格数据构建了部分线性变量含误差模型。在部分线性变量含误差的网格数据模型解释变量为固定设计的情形下,分别在单向维度观测样本容量趋于无穷和两个维度观测样本容量同时趋于无穷时对模型线性部分的未知参数、误差方差和非线性部分的未知函数进行了大样本统计推断研究。对模型线性部分未知参数和误差方差的改进的最小二乘估计量,在较弱的条件下推出估计量具有强相合性并得到收敛速度;对模型非线性部分未知函数的样条函数估计量,在一定的条件下证明了其具有强相合性并得到其收敛速度。在一定的正则条件下,分别对单向维度观测样本容量趋于无穷和两个维度观测样本容量同时趋于无穷的两种情形证明了模型线性部分未知参数和误差方差的估计量服从渐近正态分布,并对每种情形给出了渐近方差的表达式。     

方差分量的非负估计

本文对含两个方差分量的线性混合模型,给出了基于谱分解估计构造方差分量的非负估计的两种新方法,由新方法构造的非负估计在一定的条件下在均方误差意义下一致优于谱分解估计,且有显式解、计算简便。     

纵向数据下部分线性EV模型的变量选择

本文考虑了纵向数据下部分线性EV模型的变量选择问题,采用SCAD惩罚方法提出了一个变量选择过程.通过选择适当的惩罚参数,证明了该变量选择过程可以相合地识别出真实模型,并且所得的正则估计具有Orcale性质.最后模拟研究了所提出方法的有限样本性质.     

Tables for Obtaining the Best Linear Invariant Estimates of Parameters of the Weibull Distribution

A censored life-test situation is considered and the assumption of a Weibull distribution for failure times is made. Tables are given for estimating log reliable life, where the estimator is best among linear estimators with expected loss invariant under translations. These best linear invariant (BLI) estimators have uniformly smaller expected loss than the Gauss-Markov best linear unbiased (BLU) estimators and are simple linear functions of the BLU estimators. The preliminary discussion involves a comparison of the BLI estimators with other widely used estimators.     

The Construction of Good Linear Unbiased Estimates from the Best Linear Estimates for a Smaller Sample Size

A general procedure is found for constructing good unbiased linear estimators of the location and scale parameters of a distribution for use with an uncensored sample of size n.

It is presupposed that the coefficients of the best linear estimates are available for an uncensored sample of size m < n for the distribution under investigation. The coefficients of the proposed estimators are obtained as linear combinations of these with the aid of tabled values of the hypergeometric probability function.