Weibull分布基于恒加试验的参数估计

讨论了Weibull分布场合恒加寿命试验的参数估计,在文[1]对参数估计改进的基础上作了进一步改进,从而使改进后的参数估计更优.     

Weibull 分布基于恒加试验尺度参数估计

对 Weibull 分布场合恒加寿命试验的参数估计进行了讨论,在现有参数估计的基础上作了进一步改进,从而使改进后的参数估计更优.     

聚集数据线性模型的聚集广义改进双参数估计的相对效率

对于聚集数据的线性模型,提出了聚集广义改进双参数估计的概念,给出了聚集广义改进双参数估计的两种相对效率,并得到了这两种相对效率的上界.     

具有共同尺度参数的多总体指数分布的参数估计

本文讨论了具有共同尺度参数的多总体指数分布的参数估计问题；证明了尺度参数及位置参数估计的最佳仿射同变估计是不容许的，且给出相应的改进估计．     

混合系数线性回归的参数估计的改进

本文研究了未知参数向量a和随机系数β的参数估计的改进,包括在一定条件下的GLSE和LSE,并讨论了参数估计的有关性质及说明了在方差未知时,用其无偏估计代替的思想.最后对GLSE做了一些补充.     

齐次线性约束回归模型参数的主成分压缩估计

当设计矩阵X复共线时,对齐次线性约束回归模型参数的约束最小二乘估计进行改进,提出参数的主成分压缩估计,并对新参数估计的性质进行了讨论,最后进行了数值模拟,验证了算法的参数估计优于约束最小二乘估计.     

一类改进的Logistic模型参数估计方法及其应用

根据实测数据估计Logistic模型参数时,对已有的数据不满足直接利用三点法、四点法应用条件的问题,提出一类改进的三点法、四点法,即迭代逼近算法.以底部耗氧型结冰湖的溶解氧浓度分布为例,建立冰盖下溶解氧浓度垂直分布的Logistic模型,采用迭代逼近算法估计该模型的参数值.结果表明:改进的三点法、四点法的判定系数都较高,均可用于Logistic模型的参数估计,但改进的四点法整体优于改进的三点法.算法进一步完善了Logistic模型的参数估计方法.     

竞争失效产品加速寿命试验的统计分析

本文讨论了指数分布场合竞争失效产品恒定应力加速寿命试验和步进应力加速寿命试验的参数估计。对常用的最大似然估计作了改进，并用大样本结果和模拟比较说明了改进的有效性。     

截尾样本下,具有共同尺度参数的多总体指数分布的参数估计

讨论了在截尾样本下,具有共同尺度参数的多总体指数分布的参数估计问题,证明了尺度参数及位置参数的最佳仿射同变估计是不容许的,且给出了相应的改进估计.     

Pitman准则下指数分布的参数估计

本文讨论了Ｐｉｔｍａｎ准则下指数分布的参数估计问题，证明了尺度参数与位置参数的最接近仿射同变估计是ＰＣ－不容许的，并分别给出了各自的改进估计．     

混合模型中方差分量估计的容许性及非负估计

对含有两个方差分量的线性混合模型, 本文构造了方差分量的一个线性估计类, 它包含许多常见的方差分量估计. 在这个类中我们建立了容许性的必要条件, 据此得到了两个新的改进估计. 最后我们讨论了方差分量的非负估计, 得到了优于方差分析估计和Tatsuya估计的正估计.     

A Class of Biased Estimators Besed on SVD in Linear Model

In this paper,a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill-conditioning in the design matrix.Some important properties of these new estimators are obtained.By appropriate choices of the biased parameters,we construct many useful and important estimators.An application of these new estimators in three-dimensional position adjustment by distance in a spatial coordiate surveys is given.The results show that the proposed biased estimators can effectively overcome ill-conditioning and their numerical stabilities are preferable to ordinary least square estimation.     

线性模型中基于SVD的一个新的有偏估计类

§1 .　IntroductionTheproblemofill_conditioninganditsstatisticalconsequencesonalinearregressionmodelarewell_knowninstatistics(Vinod&Ullah 1981;Belsley 1991) .Itis,forinstance ,knownthatoneofthemajorconsequencesofill_conditioningontheleastsquares(LS)regressionesti matoristhattheestimatorproduceslargesamplingvariance,whichinturnmightinappropri atelyleadtoexclusionofotherwisesignificantcoefficientfromthemodel,andthesignsofcoef ficientscanbecontrarytointuitionetc..Tocircumventthisproblem ,manybi…     

有辅助信息时有限总体分布函数的新估计量

本文提出两个新的估计量,利用观察数据中的总体辅助信息来估计有限总体分布函数,并通过两个人工总体的模拟实验,比较新的估计量、传统的估计量及Rao,Kover&Mantel(1990)提出的估计量的相对平均误差与相对标准差。结果表明,从相对标准差的角度分析,两个新的估计量有一个是四个估计量中精度最好的一个,另一个也有很好的表现;而且它们在模型有所偏差时都具备了较好的稳健性。     

An improved Afriat–Diewert–Parkan nonparametric production function estimator

Recent developments in the production frontier literature include nonparametric estimators with shape constraints. A few of these estimators rely on the Afriat inequalities to provide piecewise linear approximations to the production function/frontier. We show in this paper that these Afriat–Diewert–Parkan (ADP) estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance. We propose new estimators with lower variance and a relatively low bias. We consider such alternative estimators based on (weighted) averages of random hinge functions with parameter restrictions. Small sample properties of the estimators are presented that show our new estimators outperform the existing ADP estimators when moderate to large amounts of noise are present.     

Folded overlapping variance estimators for simulation

We propose and analyze a new class of estimators for the variance parameter of a steady-state simulation output process. The new estimators are computed by averaging individual estimators from “folded” standardized time series based on overlapping batches composed of consecutive observations. The folding transformation on each batch can be applied more than once to produce an entire set of estimators. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity while the ratio of the sample size to the batch size remains constant. We give analytical and Monte Carlo results showing that, compared to their counterparts computed from nonoverlapping batches, the new estimators have roughly the same bias but smaller variance. In addition, these estimators can be computed with order-of-sample-size work.     

混合系数线性模型参数的广义Liu估计

本文研究连续测量数据情况下的混合系数线性模型的参数估计问题.利用压缩估计方法给出了该模型的一类新的有偏估计一广义Liu估计,并在均方误差意义下,证明此类估计分别优于最小二乘估计、Liu估计.最后讨论参数的选取问题.     

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.     

线性模型参数的稳健化有偏估计

本文讨论复共线性和粗差同时存在时线性模型的参数估计问题,基于等价权原理提出了一个稳健有偏估计类（稳健压缩估计）,并且建立了稳健压缩估计的计算方法,为了满足实际问题的需要,构造了许多很有意义的稳健有偏估计,例如稳健岭估计、稳健主成分估计,稳健组合主成估计、稳健单参数主成分估计、稳健根方估计等等,最后通过一个算例表明,本文提出的稳健有偏估计具有既可克服复共线性影响又可抵抗粗差干扰的良好性质。