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。     

半相依回归模型参数的协方差改进估计

本文研究了两个半相依回归系统的未知回归系数的估计问题。本文首先给出一种基于方差分量限定估计的两步协方差改进估计,并且给出了均方误差意义下优于最小二乘估计的条件。对于基于方差分量非限定估计的两步协方差改进估计,利用服从Wishart分布随机变量的可加性,本文给出了一种全新的估计形式,并且证明了该估计较文献中给出的两步协方差改进估计更加有效。     

双向分类随机效应模型中方差分量的估计

双向分类随机效应模型是一类有着广泛应用背景的统计模型,其中对模型中方差参数的一种重要估计方法是方差分析估计.由于方差分析法得到估计的均方误差(MSE)并不是最小的,本文在一类新的估计族中提出了改进的ANOVA估计.结果表明新的估计比ANOVA具有较小的MSE,这种新的估计方法可推广到医学领域中常见的一般模型.     

具有先验信息的线性模型参数估计精度影响的度量

从广义方差比，协方差迹之经以及均方误差这三个不同的度量指标刻划了用最小二乘估计代替具有先验信息的线性模型的混合估计后对估计精度的影响问题。     

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。     

方差分量模型中二次参数函数的估计

本文研究方差分量模型中均值参数的二次型和方差分量的线性型的函数的局部最优二次估计．对Ｌ．Ｒ．ＬＡＭＯＴＴＥ在文献［１］中提出的引理１进行了推广，使它更且一般性，在此基础上提出了ｒ在给定的三种关于Ｙ的平方组集合中的局部最优二次估计，并且证明了ｒ可估的充要条件．     

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．     

平衡损失函数下Cox模型的可靠性分析:记录值样本情形

本文在记录值样本下,分别讨论了一类指数分布可靠性指标的经验贝叶斯估计以及未来失效样本的预测问题.通过ML-Ⅱ方法估计超参数,进而在平衡均方损失和平衡Linex损失下,获得了相关指标的经验贝叶斯估计,并给出未来记录值样本的经验贝叶斯预测区间.利用Monte-Carlo模拟方法给出了一个数值算例,研究了结果的精确性.     

回归系数的局部根方有偏估计

线性回归模型中回归系数β的估计常用最小二乘估计(LSE)．当自变量间存在多重共线性关系时，最小二乘估计就失去了它的优良性．文提出了一种局部根方估计．证明了它的种种优良性．如容许性、相合性、Ф优良性、优效性及其对最小二乘估计抗干扰性的改进．结出了在均方误差(MSE)准则和Pitman靠近准则下该估计对通常根方估计和LSE改进的范围。     

一类双重时序模型AR(1)-MA(0)的参数矩估计及其渐近性质

近年来,人们将时间序列的研究重点,逐渐转向非线性时序模型,双重时序模型就是一类很重要的非线性模型,从目前文献来看,对非线性模型的研究主要是讨论平稳解存在的条件及模型预报问题;对于模型参数的估计及其渐近性质很少研究。 本文利用矩方法,给出了双重时序模型AR(1)-MA(O)的参数矩估计。在第二重模型噪声方差已知的条件下,通过对协方差函数渐近性质的研究,证明了该估计的相容性和渐近正态性。     

Robust Parameter Design With Computer Experiments Using Orthonormal Polynomials

Robust parameter design with computer experiments is becoming increasingly important for product design. Existing methodologies for this problem are mostly for finding optimal control factor settings. However, in some cases, the objective of the experimenter may be to understand how the noise and control factors contribute to variation in the response. The functional analysis of variance (ANOVA) and variance decompositions of the response, in addition to the mean and variance models, help achieve this objective. Estimation of these quantities is not easy and few methods are able to quantity the estimation uncertainty. In this article, we show that the use of an orthonormal polynomial model of the simulator leads to simple formulas for functional ANOVA and variance decompositions, and the mean and variance models. We show that estimation uncertainty can be taken into account in a simple way by first fitting a Gaussian process model to experiment data and then approximating it with the orthonormal polynomial model. This leads to a joint normal distribution for the polynomial coefficients that quantifies estimation uncertainty. Supplementary materials for this article are available online.     

Variance Component Calculations: Common Methods and Misapplications in the Semiconductor Industry

Calculating variance components is of utmost importance in the semiconductor industry. Often, estimates of product and process variation are needed for both qualification and improvement. Once estimates are obtained, process and product improvement efforts can proceed. In this paper, the analysis of variance (ANOVA) method is used to show how variance components are calculated correctly from a fully nested, random effects model. Due to lack of understanding and tools, other common “variance-like” calculations are often used in practice/industry, based on variances of averages, to estimate variance components. It will be shown that these calculations are misapplications of known variance formulas and provide incorrect variance component estimations. The ANOVA method will be compared to these common calculations often used in industry. The potential pitfalls often encountered with these methods will be highlighted. The adjustment factors, which correct these commonly calculated variance components to match the ANOVA method variance components, will be given and then explored. And finally, the relationships of the methods discussed herein to other nested model types will be presented. A case study will be referenced throughout the paper to show the applications of such methods.     

Approximate estimates of limiting errors of passive wireless SAW sensing with DPM

This paper discusses approximate statistical estimates of limiting errors associated with single differential phase measurement of a time delay (phase difference) between two reflectors of the passive surface acoustic wave (SAW) sensor. The remote wireless measurement is provided at the ideal coherent receiver using the maximum likelihood function approach. Approximate estimates of the mean error, mean square error, estimate variance, and Cramér-Rao bound are derived along with the error probability to exceed a threshold in a wide range of signal-to-noise ratio (SNR) values. The von Mises/Tikhonov distribution is used as an approximation for the phase difference and differential phase diversity. Simulation of the random phase difference and limiting errors also is applied.     

Zubair Lomax Distribution: Properties and Estimation Based on Ranked Set Sampling

In this article, we offer a new adapted model with three parameters, called Zubair Lomax distribution. The new model can be very useful in analyzing and modeling real data and provides better fits than some others new models. Primary properties of the Zubair Lomax model are determined by moments, probability weighted moments, Renyi entropy, quantile function and stochastic ordering, among others. Maximum likelihood method is used to estimate the population parameters, owing to simple random sample and ranked set sampling schemes. The behavior of the maximum likelihood estimates for the model parameters is studied using Monte Carlo simulation. Criteria measures including biases, mean square errors and relative efficiencies are used to compare estimates. Regarding the simulation study, we observe that the estimates based on ranked set sampling are more efficient compared to the estimates based on simple random sample. The importance and flexibility of Zubair Lomax are validated empirically in modeling two types of lifetime data.     

Effects of Fourier-plane amplitude and phase errors on image reconstruction. I. Small amplitude errors

The effects of Fourier-plane, or spectral, amplitude and phase errors on reconstructed images are studied in terms of the expected mean square error in the image. The relationship between the variance of amplitude and phase errors and the expected mean square error is derived for small amplitude errors and arbitrarily large phase errors. This allows "equivalent" amplitude and phase errors to be defined. The effects of large amplitude errors are discussed in general terms. Simulations are used to verify these relationships, and the effects of spectral amplitude and phase errors on reconstructed images are compared.     

Convergence of the optimal M-estimator over a parametric family of M-estimators

We consider a method to select an optimal M-estimator over a family of M-estimators of a parameter. Assuming that there exists an estimate of the mean square error for each element of this family of estimators, a natural estimator to consider is the M-estimator in the class which minimizes the considered estimates of the mean square errors. It is shown that under regularity conditions, this M-estimator is asymptotically normal and its asymptotic mean square error is equal to the infimum of the asymptotic mean square errors of the M-estimators in the class. We see how this method works in two different situations. In order to tackle the former problem, we present sufficient conditions for the weak convergence of a class of M-estimators.     

Estimating Component Failure Rates From Combined Component and Systems Data: Exponentially Distributed Component Lifetimes

The situation in which test results are available on systems consisting of some of k independent but nonidentical components in series is studied. The underlying distribution of the lifetime of the component is assumed to be an exponential. The method of maximum likelihood is used to obtain estimates, a chi squared approximation is used to approximate the mean and variance of the maximum likelihood estimate, and a method for reducing its bias is presented.