基于判断事后分层抽样下删失数据的保序估计

本文讨论了判断事后分层抽样下生存函数的Kaplan-Meier估计及其大样本性质.此外,基于判断事后分层抽样下各层序的信息,对样本进行保序回归,根据样本中是否存在空层的情况提出了不同的保序Kaplan-Meier估计,并讨论各估计的性质.本文通过模拟对判断事后分层样本下的各种Kaplan-Meier估计以及简单随机样本...     

对数正态分布定时截尾样本下加速寿命试验的统计分析

本文研究了定时截尾样本下加速寿命试验的统计分析,给出了各应力水平下形状参数的改进近似无偏估计（RAUE）及保序估计（IRE）,对这些估计的性质进行了讨论,最后给出的一个数值例子表明,本文提供的统计方法在计算上是简便的,在应用上是可行的。     

保序回归与最大似然估计

约束条件下的统计推断巳成为统计分析中一个重要的研究领域,而保序回归的研究又是其中之关键。本文通过一个实例引导出统计模型,比较系统地总结了保序回归的性质、求解方法,以及与最大似然估计之间的关系。本文还把问题扩展到多维保序回归和广义保序回归。     

正态分布的均值和方差分别被简单树半序和简单半序约束下的保序最大似然估计

对给定的k个正态总体，均值和方差均未知，本文讨论了均值被简单树半序约束，方差被简单半序约束下的保序最大似然估计，并给出了一个求解方法。     

Panel模型中两步估计的优良性

本文研究Panel模型中未知参数的估计问题，给出了两步估计的协方差的准确表达式．用均方误差作为度量估计的优劣标准，我们建立了两步估计优于Within估计和最小二乘估计的充要条件．特别我们获得了两步估计优于Within估计的简单充分条件．一般说来，对于中等数量的样本容量，两步估计就优于Within估计，类似的结论对Between估计或最小二乘估计也成立．     

凸规划下的保序回归

本文从约束最优化的观点来研究保序回归的解的问题 ,利用MATLAB给出了保序回归问题的求解方法 ,使得求解速度大大加快。本文的方法对进一步讲座其他保序回归问题具有一般性。     

一维马氏链保序耦合的构造

本文证明两个随机可比的一维正则马氏链必定存在保序耦合并给出了保序耦合的构造,我们也研究了一类距离下的最优耦合,证明边缘马氏链随机可比时保序耦合在该距离下最优。     

指数分布2/3(G)表决系统产品的统计分析

针对指数分布2/3(G)表决系统产品,本文给出了系统的寿命分布及数字特征,并在全样本场合下给出了参数的矩估计、极大似然估计和逆矩估计,通过大量Monte-Carlo模拟比较了三种点估计的精度。此外,还给出了求参数区间估计的两种方法,并通过大量Monte-Carlo模拟考察了区间估计的精度,得到参数的精确区间估计优于近似区间估计。     

指数分布冷贮备系统产品的统计分析——转换开关指数型的情形

给出了全样本场合下指数分布冷贮备系统产品寿命分布中参数θ≠λ时的矩估计和极大似然估计,通过Monte-Carlo给出了参数矩估计的精度,考察了1000次满足条件时所需要的模拟次数,随着样本量的增大,矩估计存在的比率逐渐增大,而极大似然估计的结果与样本有关.同时给出了参数θ=λ时的矩估计、极大似然估计和逆矩估计,通过Monte-Carlo模拟考察了参数点估计精度,认为矩估计比较优.文章还给出了求参数区间估计的两种方法——精确方法和近似方法,通过Monte-Carlo模拟认为精确方法精度较高.     

指数分布串—并联混合系统产品的统计分析

给出单元寿命服从同一指数分布的串-并联混合系统产品参数的矩估计和极大似然估计,并通过大量Monte-Carlo模拟比较了估计的精度,得到在样本容量小于35时矩估计优于极大似然估计,而样本容量不小于35时极大似然估计优于矩估计.另外,还给出了参数的精确区间估计与近似区间估计,并通过大量Monte-Carlo模拟考察了区间估计的精度.     

Structure Algorithms for Partially Ordered Isotonic Regression

Abstract

An algorithm for isotonic regression is called a structure algorithm if it searches for a “solution partition”—that is, a class of sets on each of which the isotonic regression is a constant. We discuss structure algorithms for partially ordered isotonic regression. In this article we provide a new class of structure algorithms called the isotonic block class (IBC) type algorithms. One of these is called the isotonic block class with recursion method (IBCR) algorithm, which works for partially ordered isotonic regression. It is a generalization of the pooled adjacent violators algorithm and is simpler than the min-max algorithm. We also give a polynomial time algorithm—the isotonic block class with stratification (IBCS) algorithm for matrix-ordered isotonic regression. We demonstrate the efficiency of our IBCR algorithm by using simulation to estimate the relative frequencies of the numbers of level sets of isotonic regressions on certain two-dimensional grids with the matrix order.     

Strict L<Subscript>∞</Subscript> Isotonic Regression

Given a function f and weights w on the vertices of a directed acyclic graph G, an isotonic regression of (f,w) is an order-preserving real-valued function that minimizes the weighted distance to f among all order-preserving functions. When the distance is given via the supremum norm there may be many isotonic regressions. One of special interest is the strict isotonic regression, which is the limit of p-norm isotonic regression as p approaches infinity. Algorithms for determining it are given. We also examine previous isotonic regression algorithms in terms of their behavior as mappings from weighted functions over G to isotonic functions over G, showing that the fastest algorithms are not monotonic mappings. In contrast, the strict isotonic regression is monotonic.     

The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model

When the hyperparameters of prior distribution are partly known in linear model, the simultaneous parametric empirical Bayes estimators (PEBE) of the regression coefficients and error variance are constructed. The superiority of PEBE over the least squares estimator (LSE) of regression coefficients is investigated in terms of the the mean square error matrix (MSEM) criterion, and the superiority of PEBE over LSE of the error variance is discussed under the the mean square error (MSE) criterion. Finally, when all hyperparameters are unknown, the PEBE of regression coefficients and error variance are reconstructed and the superiority of them over LSE under the MSE criterion are studied by simulation methods.     

半参数回归模型的几乎无偏岭估计

提出了半参数回归模型的几乎无偏岭估计,并与岭估计进行了比较,在均方误差意义下,几乎无偏岭估计优于岭估计. 然后讨论了有偏参数的选取问题. 最后,用模拟算例和实际应用说明了几乎无偏岭估计的有效性和可行性.     

简单半序约束下估计位置参数的一个非参方法

This paper deals with estimating parameters under simple order when samples come from location models. Based on the idea of Hodges and Lehmann estimator (H-L estimator), a new approach to estimate parameters is proposed, which is difference with the classical L1 isotonic regression and L2 isotonic regression. An algorithm to compute estimators is given. Simulations by the Monte-Carlo method is applied to compare the likelihood functions with respect to L1 estimators and weighted isotonic H-L estimators.     

缺失数据下半参数单调回归模型的估计

研究了响应变量缺失情况下半参数单调回归模型的估计问题。利用嵌入核估计的方法得到了参数部分的估计,在此基础上构造了非参数部分的单调约束最小二乘估计。证明了参数估计的渐近分布为正态分布,得到了非参数部分估计的收敛速度。通过随机模拟研究了有限样本量下估计的表现。     

基于保序回归估计的最大耐受剂量确定方法

I期临床试验研究的主要目标之一是评估药物在不同剂量水平下的毒性, 并且建议一个对病人既安全又有效的剂量, 即最大耐受剂量(MTD). 本文针对拓展的up-and-down设计, 进一步给出其基于保序回归估计的最大耐受剂量确定方法. 经大量模拟, 结果表明: 基于保序回归估计的最大耐受剂量确定方法对推荐MTD的准确性和精确度, 以及保护病人, 防止病人暴露在较高毒性剂量水平下方面实现了有意义的改善.     

Superiority of empirical Bayes estimation of error variance in linear model

In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator (PEBE) is constructed. The superiority of the PEBE over the least squares estimator (LSE) is investigated under the mean square error (MSE) criterion. Finally, some simulation results for the PEBE are obtained.     

Generalized Isotonic Regression

We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ?₂-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the l₂ algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials.     

Threshold optimization for classification in imbalanced data in a problem of gamma-ray astronomy

We introduce a method to minimize the mean square error (MSE) of an estimator which is derived from a classification. The method chooses an optimal discrimination threshold in the outcome of a classification algorithm and deals with the problem of unequal and unknown misclassification costs and class imbalance. The approach is applied to data from the MAGIC experiment in astronomy for choosing an optimal threshold for signal-background-separation. In this application one is interested in estimating the number of signal events in a dataset with very unfavorable signal to background ratio. Minimizing the MSE of the estimation is a rather general approach which can be adapted to various other applications, in which one wants to derive an estimator from a classification. If the classification depends on other or additional parameters than the discrimination threshold, MSE minimization can be used to optimize these parameters as well. We illustrate this by optimizing the parameters of logistic regression, leading to relevant improvements of the current approach used in the MAGIC experiment.