在过程监控中,使用现代工业系统中的变量进行准确有效的监控诊断仍然是一个具有挑战性的任务.本文以多元指数加权移动平均(MEWMA)策略结合一种有监督分类器(“one plus epsilon”,简称OPE分类器),提出OPE-MEWMA控制图.在考虑不同模型、...在过程监控中,使用现代工业系统中的变量进行准确有效的监控诊断仍然是一个具有挑战性的任务.本文以多元指数加权移动平均(MEWMA)策略结合一种有监督分类器(“one plus epsilon”,简称OPE分类器),提出OPE-MEWMA控制图.在考虑不同模型、偏移模式和偏移大小的情况下,探究了控制图对均值偏移的检测能力,通过比较平均运行长度等多个指标衡量控制图的性能表现.仿真结果表明,所开发的OPE-MEWMA控制图能够快速检测到均值偏移,灵敏度较高.展开更多
同时估计三个及以上同方差独立正态总体均值时,Stein[1]证明了最大似然估计平方损失下的不可容许性,并同James显式构造了具有精确一致更优风险函数的压缩型估计量.这一惊人发现——维数大于等于3时显式结构精确更优压缩型估计量——激...同时估计三个及以上同方差独立正态总体均值时,Stein[1]证明了最大似然估计平方损失下的不可容许性,并同James显式构造了具有精确一致更优风险函数的压缩型估计量.这一惊人发现——维数大于等于3时显式结构精确更优压缩型估计量——激发了大量后续研究.Statistical Sci-ence期刊2012年组织了一期专刊,“MINIMAX SHRINKAGE ESTIMATION:A TRIBUTE TO CHARLES STEIN”,表达对Stein发现的持续赞美.James和Stein[2]特定变换和Stein引理[3–4]是计算Stein估计量风险函数的两种基本途经.本文基于极坐标变换,对Stein估计量临界维数给出了解释,并提供了其风险函数计算的备用方式.极坐标变换既可以作为已有方法的补充,其本身在使用Stein引理验证绝对可积性时也发挥着重要作用.对异方差正态模型均值参数的同时估计,文献上相对缺乏兼具显式结构和精确更优风险函数的相关研究.本文在Stein原始估计量构成基础上,提出了一类显式估计量,并通过计算和观察其风险函数讨论了各待定系数的选取问题.本文为进一步认识Stein发现提供了有益补充.展开更多
In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and the...In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.展开更多
A Receiver Operating Characteristic(ROC)analysis of a power is important and useful in clinical trials.A Classical Conditional Power(CCP)is a probability of a classical rejection region given values of true treatment ...A Receiver Operating Characteristic(ROC)analysis of a power is important and useful in clinical trials.A Classical Conditional Power(CCP)is a probability of a classical rejection region given values of true treatment effect and interim result.For hypotheses and reversed hypotheses under normal models,we obtain analytical expressions of the ROC curves of the CCP,find optimal ROC curves of the CCP,investigate the superiority of the ROC curves of the CCP,calculate critical values of the False Positive Rate(FPR),True Positive Rate(TPR),and cutoff of the optimal CCP,and give go/no go decisions at the interim of the optimal CCP.In addition,extensive numerical experiments are carried out to exemplify our theoretical results.Finally,a real data example is performed to illustrate the go/no go decisions of the optimal CCP.展开更多
In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are dif...In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].展开更多
文摘在过程监控中,使用现代工业系统中的变量进行准确有效的监控诊断仍然是一个具有挑战性的任务.本文以多元指数加权移动平均(MEWMA)策略结合一种有监督分类器(“one plus epsilon”,简称OPE分类器),提出OPE-MEWMA控制图.在考虑不同模型、偏移模式和偏移大小的情况下,探究了控制图对均值偏移的检测能力,通过比较平均运行长度等多个指标衡量控制图的性能表现.仿真结果表明,所开发的OPE-MEWMA控制图能够快速检测到均值偏移,灵敏度较高.
文摘同时估计三个及以上同方差独立正态总体均值时,Stein[1]证明了最大似然估计平方损失下的不可容许性,并同James显式构造了具有精确一致更优风险函数的压缩型估计量.这一惊人发现——维数大于等于3时显式结构精确更优压缩型估计量——激发了大量后续研究.Statistical Sci-ence期刊2012年组织了一期专刊,“MINIMAX SHRINKAGE ESTIMATION:A TRIBUTE TO CHARLES STEIN”,表达对Stein发现的持续赞美.James和Stein[2]特定变换和Stein引理[3–4]是计算Stein估计量风险函数的两种基本途经.本文基于极坐标变换,对Stein估计量临界维数给出了解释,并提供了其风险函数计算的备用方式.极坐标变换既可以作为已有方法的补充,其本身在使用Stein引理验证绝对可积性时也发挥着重要作用.对异方差正态模型均值参数的同时估计,文献上相对缺乏兼具显式结构和精确更优风险函数的相关研究.本文在Stein原始估计量构成基础上,提出了一类显式估计量,并通过计算和观察其风险函数讨论了各待定系数的选取问题.本文为进一步认识Stein发现提供了有益补充.
基金supported by the National Natural Science Foundation of China(Grant No.12301603).
文摘In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.
基金supported by the National Social Science Fund of China(Grand No.21XTJ001).
文摘A Receiver Operating Characteristic(ROC)analysis of a power is important and useful in clinical trials.A Classical Conditional Power(CCP)is a probability of a classical rejection region given values of true treatment effect and interim result.For hypotheses and reversed hypotheses under normal models,we obtain analytical expressions of the ROC curves of the CCP,find optimal ROC curves of the CCP,investigate the superiority of the ROC curves of the CCP,calculate critical values of the False Positive Rate(FPR),True Positive Rate(TPR),and cutoff of the optimal CCP,and give go/no go decisions at the interim of the optimal CCP.In addition,extensive numerical experiments are carried out to exemplify our theoretical results.Finally,a real data example is performed to illustrate the go/no go decisions of the optimal CCP.
基金supported by the National Natural Science Foundation of China(Grant No.11671145)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).
文摘In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].