有限理性与多目标最优化问题弱有效解集的稳定性

本文对多目标最优化问题定义了理性函数,证明了大多数的多目标最优化问题都是结构稳定和鲁棒的。     

包含测度的椭圆方程解的最大模的估计

对包含测度的椭圆方程 ,证明解的有界性已颇为困难 ,对解的最大模作出估计尤其困难。本文只对其中一种特殊情形作出解最大模的先验估计。     

收益率分布主观模型及其实证分析

在累积展望理论基础上,通过累积概率描述主观因素对内在价值分布的影响,建立收益率分布主观模型。建立从经验收益率数据中估计投资群体的风险追求程度、投资情绪和非完全理性程度等行为变量参数的方法。利用沪市A股数据,进行χ2同分布拟合检验,结果表明:0.05水平下,沪市69.56%股票的收益率分布认为符合收益率分布主观模型,接受t分布、双正态混合分布、稳定分布和正态分布假设的股票分别为56.31%、44.80%、46.06%和1.74%。通过比较大、小公司投资群体的行为差异,以及利用收益率主观模型估计的内在价值信息参数和行为参数对截面个股收益率进行解释的实证分析,表明收益率分布主观模型及估计行为参数的方法具有合理性。     

求解输出为有界随机数的排序择优问题

目的/意义排序择优问题是仿真优化领域的经典研究问题。该问题的目标是设计统计采样算法,通过在有限个统计分布中进行采样并观测随机采样结果从而找到真实均值最大的分布。在该问题的研究中,现有文献大多假设对不同分布进行采样时输出为正态分布随机数,进而基于正态分布随机数相关性质进行算法设计。但在现实中,该假设通常不成立,一旦假设不成立,现有算法的统计有效性将会大受影响。设计/方法将正态假设进行拓展,即假设对不同分布为有界域分布,进而开展算法设计。结论/发现设计出一类顺序淘汰式算法求解输出为有界域随机数的排序择优问题,数值实验验证,此算法效率远高于现有的SE、ME和lil′DCB算法。     

A Robust and Almost Fully Efficient M-Estimator

Simultaneous robust estimates of location and scale parameters are derived from a class of M-estimating equations. A coefficient p ( p > 0), which plays a role similar to that of a tuning constant in the theory of M-estimation, determines the estimating equations. These estimating equations may be obtained as the gradient of a strictly convex criterion function. This article shows that the estimators are uniquely defined, asymptotically bi-variate normal and have positive breakdown for some choices of p . When p = 0.12 and p = 0.3, the estimators are almost fully efficient for normal and exponential distributions: efficiencies with respect to the maximum likelihood estimators are 1.00 and 0.99, respectively. It is shown that the location estimator for known scale has the maximum breakdown point 0.5 independent of p , when the target model is symmetric. Also it is shown that the scale estimator has a positive breakdown point which depends on the choice of p . A simulation study finds that the proposed location estimator has smaller variance than the Hodges–Lehmann estimator, Huber's minimax and bisquare M-estimators.     

一类双非线性抛物组解的有界性

考虑一类对角型双非线性抛物组，在1＜p＜2的情形在合适的假定下证明了广义解的有界性。     

Robust regression through robust covariances

This paper discusses the estimation of regression parameters after summarizing the data by a covariance matrix of the concatenated vector of explanatory variables and response variable. A robust estimate of the covariance matrix leads to a robust regression estimator. An M-estimator at the covariance estimation step is studied in the paper, and the resulting regression estimator is compared to a few previously proposed robust regression estimators.     

Use of asymmetric loss functions in sequential estimation problems for multiple linear regression

When estimating in a practical situation, asymmetric loss functions are preferred over squared error loss functions, as the former is more appropriate than the latter in many estimation problems. We consider here the problem of fixed precision point estimation of a linear parametric function in beta for the multiple linear regression model using asymmetric loss functions. Due to the presence of nuissance parameters, the sample size for the estimation problem is not known beforehand and hence we take the recourse of adaptive multistage sampling methodologies. We discuss here some multistage sampling techniques and compare the performances of these methodologies using simulation runs. The implementation of the codes for our proposed models is accomplished utilizing MATLAB 7.0.1 program run on a Pentium IV machine. Finally, we highlight the significance of such asymmetric loss functions with few practical examples.     

关于Menger概率赋范空间上线性算子的共鸣定理

提出 Menger 概率赋范线性空间上集合有界性的简化定义,利用 Menger概率赋范空间的线性拓扑性质,在较弱的 t-模条件下,建立了概率有界、概率半有界、非概率无界意义下线性算子的共鸣定理。     

考虑消费者有限理性的体验式商品订购与库存配给策略

退货遗忘与缺货后悔是消费者在现实中普遍存在的有限理性行为。在考虑这两种有限理性行为以及销售商提供无理由退款承诺的基础上,构建了一个两期模型对体验式商品的订购与库存配给策略进行了分析。研究得到如下结论：首先,只有当产品价值的上界大于某个临界值时,消费者才会在两个销售期内购买产品,销售商应该采取库存配给策略以应对消费者的策略行为;其次,销售商的收益随着消费者满意概率、退货遗忘率和缺货后悔程度的增大而增大。数值分析表明：当消费者满意概率或产品满足率感知偏差较大时,消费者策略行为的负面影响在一定程度上得到减轻;虽然有限理性总是可以提高销售商的收益,但是退货遗忘与缺货后悔对销售商收益增长的影响作用是不同的。