Weibull分布形状参数的收缩估计

本文研究两参数Weibull分布在Ⅱ形截尾场合下形状参数的收缩估计．提出了形状参数的四个不同的收缩估计，在Minimax遗憾准则下得到了最优收缩系数．通过对这四个收缩信计的效的研究，可知他们在适当的先验信息下都优于原来的估计，其中基于近似无偏估计所得的形状参数的无编估计是比较理想的估计量．     

熵损失函数下两参数指数威布尔分布尺度参数的Bayes估计

本文给定一截尾样本，在熵损失函数下，研究了两参数指数威布尔分布尺度参数在先验伽玛分布下的Bayes估计，并给出了该参数的Bayes区间估计。     

双指数分布位置参数的经验Bayes估计问题

本文在平方损失下导出了双指数分布位置参数的Bayes估计，利用非参数方法构造了位置参数的经验Bayes(EB)估计．在适当的条件下，获得了EB估计的收敛速度．最后，给出了一个例子说明适合定理条件的先验分布是存在的．     

位置参数受约束时指数分布在定数截尾样本下的参数估计

本文考虑指数分布在定数截尾样本情况下位置多数有上界约束时，位置多数和尺度参数的估计．分别给出了有约束位置参数和尺度参数的最佳仿射同变估计在均方误基原则下的改进估计，同时研究了在Pitman准则下这些估计的比较，观察到了与均方误差原则不一致，甚至矛盾的结论．最后应用到位置参数有顺序的两个截尾指数分布，同样获得类同结果．     

连续型多参数指数族参数的经验Bayes估计的收敛速度

本文用一般的最近邻型估计的方法研究了连续型多参数指数族参数的经验Ｂａｙｅｓ估计，在通常的条件下，给出了估计的较理想的收敛速度．     

线性模型中不可估参数的线性估计的可容许性

对一般线性模型在平方损失函数下，得到了一维不可估参数函数的线性估计为可容许估计的充要条件，以及模型中参数向量（非线性可估）的线性估计为可容许估计的两个充要条件，并得到了多维参数函数（可估或不可估）的线性估计为可容许估计的一个充分条件以及特殊情况下的一个充要条件．     

截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文[1]给出了参数λ在先验分布为Г(α，β)分布的假设下的Bayes估计．文[3]给出了在平方损失下的Bayes估计,本文讨论先验分布为B(a，b)分布时，参数λ的Bayes估计。     

定时截尾场合下双参数指数分布的参数估计

本文给出了定量截尾场合下双参数指数分布中两个参数的近似无偏估计（AUE），计算了它们的期望及方差，并与极大似然估计，相应定数截尾场合下的估计做了比较。     

截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文［１］给出了参数λ在先验分布为Γ（α，β）分布的假设下的Ｂａｙｅｓ估计．文［３］给出了在平方损失下的Ｂａｙｅｓ估计．本文讨论先验分布为Ｂ（ａ，ｂ）分布时，参数λ的Ｂａｙｅｓ估计．     

半参数变量含误差函数关系模型的小波估计

本文研究半参数变量含误差函数关系模型，应用小波估计法和全最小二乘法得出未知参数和未知函数的估计，在一般的条件下，证明了估计的强相合性、一致强相合性，并给出了误差方差估计的强收敛速度。     

Second derivative estimation using harmonic analysis

Simulation sensitivity analysis is an important problem for simulation practitioners analyzing complex systems. The significance of this problem has resulted in the development of various gradient estimators that can be used to address this issue. Although higher derivative estimators have been discussed concurrently, less attention has been given to assess the efficiency and feasibility of computing such estimators. In this paper, two second derivative estimators are presented. The first estimators, called the HFD estimators, combine harmonic gradient estimators with finite differences second derivative estimators. The resulting hybrid estimators requireO(p) fewer simulation runs to implement compared to the straightforward finite differences approach, wherep is the number of input parameters in the simulation model. The second estimators, called the HA estimators, incorporate harmonic analysis directly, requiring one or two simulation runs to implement, depending on whether a control variate simulation run is made. Expressions for the bias and the variance of the HFD and the HA estimators (with and without variance reduction techniques) are derived. Optimal mean squared error convergence rates are also discussed. In particular, the convergence rates for both these estimators are shown to be the same, though the computational performance of the HFD estimators is better than that for the HA estimators on anM/M/1 queue simulation model. Computational results for the HFD estimators on an (s, S) inventory system simulation model are also included.     

Safe and tight linear estimators for global optimization

Global optimization problems are often approached by branch and bound algorithms which use linear relaxations of the nonlinear constraints computed from the current variable bounds. This paper studies how to derive safe linear relaxations to account for numerical errors arising when computing the linear coefficients. It first proposes two classes of safe linear estimators for univariate functions. Class-1 estimators generalize previously suggested estimators from quadratic to arbitrary functions, while class-2 estimators are novel. When they apply, class-2 estimators are shown to be tighter theoretically (in a certain sense) and almost always tighter numerically. The paper then generalizes these results to multivariate functions. It shows how to derive estimators for multivariate functions by combining univariate estimators derived for each variable independently. Moreover, the combination of tight class-1 safe univariate estimators is shown to be a tight class-1 safe multivariate estimator. Finally, multivariate class-2 estimators are shown to be theoretically tighter (in a certain sense) than multivariate class-1 estimators.     

Flexible Multivariate Density Estimation With Marginal Adaptation

This article is concerned with multivariate density estimation. We discuss deficiencies in two popular multivariate density estimators—mixture and copula estimators, and propose a new class of estimators that combines the advantages of both mixture and copula modeling, while being more robust to their weaknesses. Our method adapts any multivariate density estimator using information obtained by separately estimating the marginals. We propose two marginally adapted estimators based on a multivariate mixture of normals and a mixture of factor analyzers estimators. These estimators are implemented using computationally efficient split-and-elimination variational Bayes algorithms. It is shown through simulation and real-data examples that the marginally adapted estimators are capable of improving on their original estimators and compare favorably with other existing methods. Supplementary materials for this article are available online.     

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.     

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.     

Simultaneous Estimation of Several Intraclass Correlation Coefficients

Based on shrinkage and preliminary test rules, various estimators are proposed for estimation of several intraclass correlation coefficients when independent samples are drawn from multivariate normal populations. It is demonstrated that the James-Stein type estimators are asymptotically superior to the usual estimators. Furthermore, it is also indicated through asymptotic results that none of the preliminary test and shrinkage estimators dominate each other, though they perform relatively well as compared to the classical estimator. The relative dominance picture of the estimators is presented. A Monte Carlo study is performed to appraise the properties of the proposed estimators for small samples.     

Estimating hazard ratios in nested case-control studies by mantel-haenszel method

1. IntroductionConsider a follow-up study which is carried out to investigate the association betweenexposure variables and mortality rate in a cohort. In the case where the cohort is of 1argesise, the complete follow-up ndght be too expensive or difficult, and various nested samplingmethod8 have been suggested by Thomas[l], Prenti..[2] 5 Goldstein and Langholzl'] and otherauthors. Most of the authors employ Coxl4] regression mode1 for estimating the hazard ratio8of exposures.Now a well-reco…     

Bayesian inference using record values from Rayleigh model with application

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.     

Robust weighted orthogonal regression in the errors-in-variables model

This paper focuses on robust estimation in the structural errors-in-variables (EV) model. A new class of robust estimators, called weighted orthogonal regression estimators, is introduced. Robust estimators of the parameters of the EV model are simply derived from robust estimators of multivariate location and scatter such as the M-estimators, the S-estimators and the MCD estimator. The influence functions of the proposed estimators are calculated and shown to be bounded. Moreover, we derive the asymptotic distributions of the estimators and illustrate the results on simulated examples and on a real-data set.     

广义偏最小二乘(PLS)估计类

本文研究了一类含有偏最小二乘（partialleastsquaresPLS）估计的估计类．给出了PLS估计的一般代数形式；讨论了含有PLS估计的广义PPLS估计类的统计性质；给出了该估计类优于最小二乘估计的条件．