相协样本下Wilcoxon两样本统计量的渐近分布北大核心CSCD

研究了相协样本下Wilcoxon两样本统计量的渐近分布的问题.利用Hoeffding分解方法,获得了相协样本下Wilcoxon两样本统计量的渐近分布为正态分布的结果,推广了负相协样本下Wilcoxon两样本统计量的渐近分布的结果.     

相协样本下Wilcoxon两样本统计量的渐近分布

研究了相协样本下Wilcoxon两样本统计量的渐近分布的问题.利用Hoeffding分解方法,获得了相协样本下Wilcoxon两样本统计量的渐近分布为正态分布的结果,推广了负相协样本下Wilcoxon两样本统计量的渐近分布的结果.     

相协样本下概率密度函数的调整经验似然推断

本文研究相协样本下概率密度函数的调整经验似然推断,证明对数调整经验似然比统计量服从χ²分布,由此构造了相协样本下概率密度函数的调整经验似然置信区间.在有限样本情况下通过数值模拟,对比分析得到AEL的表现略优于EL和NA的表现.     

考虑新增样本的中国上市公司马尔科夫分析

使用吸收马尔科夫链对中国上市公司的未来经营状况进行了分析和预测.在前人研究的基础上,本文将相应的分析进行了扩展,考虑了新增样本情况下的上市公司整体经营状况.实证研究表明,考虑新增样本情况下的上市公司整体经营状况与不考虑此因素的结果稍有不同,而这正反映了新增样本的影响.     

强混合样本下部分线性模型的经验似然推断（英文）

本文研究强混合样本下部分线性模型的经验似然推断,将分块技术应用到经验似然方法中,证明部分线性模型的参数β的对数经验似然比统计量的渐近分布为卡方分布,由此构造强混合样本下β的经验似然置信区间.在有限样本情况下给出数值模拟结果.     

强混合样本下随机设计情形线性模型的经验似然推断

本文研究强混合样本下随机设计情形线性模型的经验似然推断,将分块技术应用到经验似然方法中,证明了线性模型的参数β的对数经验似然比统计量的渐近分布为卡方分布,由此构造了强混合样本下β的经验似然置信区间.在有限样本情况下给出数值模拟结果.     

强混合样本下最近邻密度估计的渐近正态性

研究了α-混合样本下最近邻密度估计的渐近性质,证明了估计的渐近正态性并且给出了其渐近方差的显式表达式,由此构造了α-混合样本下概率密度的渐近置信区间.     

单纯随机抽样理论之我见

针对一般经济统计教材中普遍存在的关于单纯随机抽样过程中,不同抽样方法下样本方差的无偏性问题提出自己的见解.认为,抽样理论源于实践,重复抽样时有Nn个样本、不重复抽样时有CnN个样本是实际抽样调查工作中普遍采用的方式、方法,更是单纯随机抽样推断理论的源泉.在此基础上数学界将实际工作中各种可能始点的抽样方法赋予理性思考、研究,获得结论:无限制抽样和简单随机抽样条件下样本方差是总体方差的无偏估计量.     

广义指数分布下恒定应力加速寿命试验的贝叶斯分析

研究产品寿命服从广义指数分布的有关加速寿命试验的贝叶斯统计分析.首先介绍了广义指数分布在恒定应力下的加速寿命试验基本过程;其次在完全样本,和定数截尾样本下,分别给出了广义指数分布参数的贝叶斯估计;最后运用随机模拟方法对各种估计结果的优良性进行了分析比较.     

截断样本下的强率函数和密度函数核估计的渐进正态性

本文用[1]发展的计数过程去研究截断样本下强率函数核估计的渐进正态性．在弱于[7]和[10]的条件下，得到了更一般的结果．接着我们将这种方法运用到密度函数核估计，在较弱的条件下，得到了截断样本下密度函数核估计的渐进正态性．     

相依数据下一般函数核估计的一致收敛速度

不论数据是独立的还是相依的,在非参数和半参数模型中,都涉及到对未知均值函数或者对某函数的未知条件期望的估计.本文针对这一问题,在比较弱的条件下,给出在数据是α-混合相依时一般函数的条件数学期望的估计,并讨论了它的一致收敛速度.     

Weibull 分布等分位数数据填充算法及其应用

基于作者曾提出的处理非随机删失数据的迭代算法,针对weibull分布相同定时截尾型试验数据,通过改变数据的填补方式,在保证由算法所得的参数估计的相合性和不变性的前提下,使得改进后的算法所得的虚拟完全数据更接近于真实的完全数据.模拟研究表明,对于删失数据情形下可靠度的区间估计问题,改进后的算法更加精确.     

Asymptotic comparison of semi-supervised and supervised linear discriminant functions for heteroscedastic normal populations

It has been reported that using unlabeled data together with labeled data to construct a discriminant function works successfully in practice. However, theoretical studies have implied that unlabeled data can sometimes adversely affect the performance of discriminant functions. Therefore, it is important to know what situations call for the use of unlabeled data. In this paper, asymptotic relative efficiency is presented as the measure for comparing analyses with and without unlabeled data under the heteroscedastic normality assumption. The linear discriminant function maximizing the area under the receiver operating characteristic curve is considered. Asymptotic relative efficiency is evaluated to investigate when and how unlabeled data contribute to improving discriminant performance under several conditions. The results show that asymptotic relative efficiency depends mainly on the heteroscedasticity of the covariance matrices and the stochastic structure of observing the labels of the cases.     

On the finite time blow-up for filtration problems with nonlinear reaction

We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow-up of solutions subject to sufficiently large initial data provided that the reaction term “overpowers” the nonlinear diffusion in a certain sense. Secondly, under related assumptions on the nonlinearities, we show that initial data above positive stationary state solutions will always lead to finite time blow-up.     

Rank-Score Tests in Factorial Designs with Repeated Measures

Nonparametric factorial designs for multivariate observations are considered under the framework of general rank-score statistics. Unlike most of the literature, we do not assume the continuity of the underlying distribution functions. The models studied include general repeated measures designs, compound symmetry designs, and designs for longitudinal data. In particular, designs for ordered categorical data are included. The vectors of the multivariate observations may have different lengths. Moreover, our general framework includes missing values and singular covariance matrices which occur quite frequently in practical data analysis problems. The asymptotic properties of the proposed statistics are studied under general nonparametric hypotheses as well as under a sequence of nonparametric contiguous alternatives. L₂-consistent estimators for the unknown covariance matrices are given and two types of quadratic forms are considered for testing the nonparametric hypotheses. The results are applied to a two-way mixed model assuming compound symmetry and to a factorial design for longitudinal data. The main idea of the proofs is based on some moment inequalities for empirical distribution functions in mixed models. The details are provided in the Appendix.     

Robust economic order quantity models

In this paper, we study the classical economic order quantity (EOQ) model under significant. In particular, the problem under consideration is the economic order quantity model with the input data of the demand rate, the order cost, and the holding cost rate being uncertain. A robustness approach based on scenario characterization of the input data is adopted to describe the uncertainties. The aim of the approach is to find an inventory policy that performs well under all realizable input data scenarios. An efficient linear time algorithm is devised to find the robust decisions. Analytical results are obtained for the case where input data are defined in continuous intervals. Comparisons on performances between the robust decisions and the stochastic optimization decisions are conducted. The results demonstrate the advantages of robustness approach.     

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.     

非参数回归函数估计的渐近正态性

本文研究了独立或相依样本时非参数回归函数的Ｎａｄａｒａｙａ-Ｗａｔｓｏｎ估计，在简洁合理的条件下，证明了估计量的渐近正态性．获得的结论可在时间序列分析中得到应用．     

A more powerful test identifying the change in mean of functional data

An existence of change point in a sequence of temporally ordered functional data demands more attention in its statistical analysis to make a better use of it. Introducing a dynamic estimator of covariance kernel, we propose a new methodology for testing an existence of change in the mean of temporally ordered functional data. Though a similar estimator is used for the covariance in finite dimension, we introduce it for the independent and weakly dependent functional data in this context for the first time. From this viewpoint, the proposed estimator of covariance kernel is more natural one when the sequence of functional data may possess a change point. We prove that the proposed test statistics are asymptotically pivotal under the null hypothesis and consistent under the alternative. It is shown that our testing procedures outperform the existing ones in terms of power and provide satisfactory results when applied to real data.     

青藏高原不同半径热融湖下融区发展差异的非线性分析

以青藏高原北麓河地区的气象资料、热融湖信息和冻土监测数据为基础,以柱坐标系下伴有相变的热传导方程为模型,在假设不同半径热融湖湖底温度和湖水深度相同条件下,模拟了不同半径热融湖对湖下多年冻土热状况和融区发展长期影响的差异.计算结果表明,不同半径热融湖湖下土壤热状况和融区发展都有较大差异,精确模拟热融湖下土壤热状况和融区发展的数学模型必须考虑热融滑塌引起的热融湖横向扩展作用.