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学者姓名：李寿梅
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Abstract ：
In this paper, we consider filtration-consistent nonlinear expectations which satisfy a general domination condition. We show that filtration-consistent nonlinear expectations can be represented byg-expectations defined by the solutions of backward stochastic differential equations, whose generators are independent ofyand uniformly continuous inz. As an application, we establish a concentration inequality for time-consistent risk measures.
Keyword ：
Filtration-consisitent expectation Filtration-consisitent expectation Time-consistent risk measure Time-consistent risk measure g-expectation g-expectation Doob-Meyer decomposition Doob-Meyer decomposition Backward stochastic differential equation Backward stochastic differential equation
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| GB/T 7714 | Zheng, Shiqiu , Li, Shoumei . A representation for filtration-consistent nonlinear expectations and its application [J]. | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION , 2020 , 51 (12) : 7133-7150 . |
| MLA | Zheng, Shiqiu 等. "A representation for filtration-consistent nonlinear expectations and its application" . | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 51 . 12 (2020) : 7133-7150 . |
| APA | Zheng, Shiqiu , Li, Shoumei . A representation for filtration-consistent nonlinear expectations and its application . | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION , 2020 , 51 (12) , 7133-7150 . |
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Abstract ：
Linear regression models for interval-valued data have been widely studied. Most literatures are to split an interval into two real numbers, i.e., the left- and right-endpoints or the center and radius of this interval, and fit two separate real-valued or two dimension linear regression models. This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix, based on a generalized linear model for interval-valued data. A three step estimation method is proposed. Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.
Keyword ：
interval-valued data interval-valued data weighted least squares estimation weighted least squares estimation truncated normal distribution truncated normal distribution order constraint order constraint Conditional maximum likelihood estimation Conditional maximum likelihood estimation
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| GB/T 7714 | Zhong, Yu , Zhang, Zhongzhan , Li, Shoumei . A Constrained Interval-Valued Linear Regression Model: A New Heteroscedasticity Estimation Method [J]. | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2020 , 33 (6) : 2048-2066 . |
| MLA | Zhong, Yu 等. "A Constrained Interval-Valued Linear Regression Model: A New Heteroscedasticity Estimation Method" . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 33 . 6 (2020) : 2048-2066 . |
| APA | Zhong, Yu , Zhang, Zhongzhan , Li, Shoumei . A Constrained Interval-Valued Linear Regression Model: A New Heteroscedasticity Estimation Method . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2020 , 33 (6) , 2048-2066 . |
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Abstract ：
研究集值多元时间序列的一些初步的理论,这为拓广经典的多元时间序列模型提供了理论基础.首先,基于集值理论,进一步提出集值向量、集值随机向量的定义,并给出集值随机向量的期望向量、交叉协方差阵与交叉相关阵的定义与性质.然后,在此基础上,给出集值多元时间序列的定义,并研究关于集值多元时间序列的平稳性,期望向量、交叉协方差阵和交叉相关阵的定义及性质,讨论平稳的集值多元时间序列的最优线性预测问题.最后,在集值多元时间序列的基础之上,讨论区间值多元时间序列,并建立区间值多元自回归模型.模拟研究与实证分析验证了该模型与所提出方法的合理性.
Keyword ：
交叉相关阵 交叉相关阵 集值多元时间序列 集值多元时间序列 平稳性 平稳性 交叉协方差阵 交叉协方差阵 区间值多元自回归模型 区间值多元自回归模型 集值随机向量 集值随机向量
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| GB/T 7714 | 钟钰 , 李寿梅 , 章磊 . 集值和区间值的多元时间序列 [J]. | 北京工业大学学报 , 2020 , 46 (2) : 208-216 . |
| MLA | 钟钰 等. "集值和区间值的多元时间序列" . | 北京工业大学学报 46 . 2 (2020) : 208-216 . |
| APA | 钟钰 , 李寿梅 , 章磊 . 集值和区间值的多元时间序列 . | 北京工业大学学报 , 2020 , 46 (2) , 208-216 . |
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Abstract ：
单个聚类方法得到的结果会存在不稳定性等问题,为了克服这些问题,本文在证据理论(又称为信任函数理论)的基础上提出了一种新的聚类集成方法.多数情况下,聚类集成方法主要包含2个关键步骤:得到一组基划分,以及结合基划分得到最终聚类结果,本文的方法重点考虑第2步.在第1步得到基划分之后,将其转换成一种中间表示,可以称这种中间表示为关系表示.在证据理论中,我们认为得到的关系表示是不可靠的,可以周折扣过程对关系表示进行预处理,然后就可以用不同的结合法则融合关系表示.从融合后的关系表示中提取信任矩阵或似然矩阵,将其视为样本间的互相关矩阵.为了能够充分利用样本间的传递性,将得到的互相关矩阵视为一个模糊关系,对其做传递闭包处理,从而得到一个模糊等价关系.将模糊的等价关系视为新的相似性数据,用能够处理相似性数据的聚类方法得到最终的结果.通过实验,表明了该聚类集成方法的稳定性和有效性.
Keyword ：
关系表示 关系表示 互相关矩阵 互相关矩阵 证据理论 证据理论 聚类集成 聚类集成 传递闭包 传递闭包
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| GB/T 7714 | 李锋 , 李寿梅 , Thierry Denoeux . 基于证据理论的聚类集成方法 [J]. | 南京信息工程大学学报 , 2019 , 11 (3) : 332-339 . |
| MLA | 李锋 等. "基于证据理论的聚类集成方法" . | 南京信息工程大学学报 11 . 3 (2019) : 332-339 . |
| APA | 李锋 , 李寿梅 , Thierry Denoeux . 基于证据理论的聚类集成方法 . | 南京信息工程大学学报 , 2019 , 11 (3) , 332-339 . |
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Abstract ：
Different companies may not be allowed to treat data together given restrictions of security, privacy or other technical reasons. In order to make better use of information from different sources, clustering algorithms based on collaboration mechanisms have been widely used. We propose the concept of collaborative evidential clustering under the framework of evidence theory. The key point is to establish collaboration among the credal partition matrices of each data site to meet the data confidentiality requirements. Considering the problems of excessive information interaction and insufficient information interaction, we design single-step and multi-step collaborative evidential clustering algorithms. Our algorithms were validated on real data sets.
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| GB/T 7714 | Qiao, Yixuan , Li, Shoumei , Denoeux, Thierry . Collaborative Evidential Clustering [C] . 2019 : 518-530 . |
| MLA | Qiao, Yixuan 等. "Collaborative Evidential Clustering" . (2019) : 518-530 . |
| APA | Qiao, Yixuan , Li, Shoumei , Denoeux, Thierry . Collaborative Evidential Clustering . (2019) : 518-530 . |
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Abstract ：
单个聚类方法得到的结果会存在不稳定性等问题,为了克服这些问题,本文在证据理论(又称为信任函数理论)的基础上提出了一种新的聚类集成方法.多数情况下,聚类集成方法主要包含2个关键步骤:得到一组基划分,以及结合基划分得到最终聚类结果,本文的方法重点考虑第2步.在第1步得到基划分之后,将其转换成一种中间表示,可以称这种中间表示为关系表示.在证据理论中,我们认为得到的关系表示是不可靠的,可以用折扣过程对关系表示进行预处理,然后就可以用不同的结合法则融合关系表示.从融合后的关系表示中提取信任矩阵或似然矩阵,将其视为样本间的互相关矩阵.为了能够充分利用样本间的传递性,将得到的互相关矩阵视为一个模糊关系,对其...
Keyword ：
传递闭包 传递闭包 证据理论 证据理论 关系表示 关系表示 聚类集成 聚类集成 互相关矩阵 互相关矩阵
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| GB/T 7714 | 李锋 , 李寿梅 , Thierry Denoeux . 基于证据理论的聚类集成方法 [J]. | 南京信息工程大学学报(自然科学版) , 2019 , 11 (03) : 332-339 . |
| MLA | 李锋 等. "基于证据理论的聚类集成方法" . | 南京信息工程大学学报(自然科学版) 11 . 03 (2019) : 332-339 . |
| APA | 李锋 , 李寿梅 , Thierry Denoeux . 基于证据理论的聚类集成方法 . | 南京信息工程大学学报(自然科学版) , 2019 , 11 (03) , 332-339 . |
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Abstract ：
In this paper, we establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation.
Keyword ：
representation theorem of generator representation theorem of generator converse comparison theorem converse comparison theorem g-expectation g-expectation backward stochastic differential equation backward stochastic differential equation
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| GB/T 7714 | Zheng, Shi-qiu , Li, Shou-mei . Representation Theorem for Generators of Quadratic BSDEs [J]. | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2018 , 34 (3) : 622-635 . |
| MLA | Zheng, Shi-qiu 等. "Representation Theorem for Generators of Quadratic BSDEs" . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 34 . 3 (2018) : 622-635 . |
| APA | Zheng, Shi-qiu , Li, Shou-mei . Representation Theorem for Generators of Quadratic BSDEs . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2018 , 34 (3) , 622-635 . |
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Abstract ：
In this paper, we study the problem of the suppression of explosion by noise for nonlinear non-autonomous differential systems. For a deterministic non-autonomous differential system dx(t) = f(x(t), t)dt, which can explode at a finite time, we introduce polynomial noise and study the perturbed system dx(t) = f(x(t), t)dt + h(t) (12) |x(t)| Ax(t)dB(t). We demonstrate that the polynomial noise can not only guarantee the existence and uniqueness of the global solution for the perturbed system, but can also make almost every path of the global solution grow at most with a certain general rate and even decay with a certain general rate (including super-exponential, exponential, and polynomial rates) under specific weak conditions.
Keyword ：
non-autonomous differential system non-autonomous differential system explosion suppression explosion suppression noise noise growth with general rate growth with general rate general polynomial growth condition general polynomial growth condition decay with general rate decay with general rate
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| GB/T 7714 | Feng, Lichao , Li, Shoumei , Song, Renming et al. Suppression of explosion by polynomial noise for nonlinear differential systems [J]. | SCIENCE CHINA-INFORMATION SCIENCES , 2018 , 61 (7) . |
| MLA | Feng, Lichao et al. "Suppression of explosion by polynomial noise for nonlinear differential systems" . | SCIENCE CHINA-INFORMATION SCIENCES 61 . 7 (2018) . |
| APA | Feng, Lichao , Li, Shoumei , Song, Renming , Li, Yemo . Suppression of explosion by polynomial noise for nonlinear differential systems . | SCIENCE CHINA-INFORMATION SCIENCES , 2018 , 61 (7) . |
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Abstract ：
A system of dynamically consistent nonlinear evaluation (-evaluation) provides an ideal characterization for the dynamical behaviors of risk measures and the pricing of contingent claims. The purpose of this paper is to study the representation for the -evaluation by the solution of a backward stochastic differential equation (BSDE). Under a general domination condition, we prove that any -evaluation can be represented by the solution of a BSDE with a generator which is Lipschitz in y and uniformly continuous in z.
Keyword ：
Nonlinear evaluation Nonlinear evaluation Backward stochastic differential equation Backward stochastic differential equation g-evaluation g-evaluation g-expectation g-expectation Nonlinear expectation Nonlinear expectation
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| GB/T 7714 | Zheng, Shiqiu , Li, Shoumei . On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case [J]. | JOURNAL OF THEORETICAL PROBABILITY , 2018 , 31 (1) : 119-158 . |
| MLA | Zheng, Shiqiu et al. "On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case" . | JOURNAL OF THEORETICAL PROBABILITY 31 . 1 (2018) : 119-158 . |
| APA | Zheng, Shiqiu , Li, Shoumei . On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case . | JOURNAL OF THEORETICAL PROBABILITY , 2018 , 31 (1) , 119-158 . |
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Abstract ：
In evidential clustering, cluster-membership uncertainty is represented by Dempster-Shafer mass functions. The notion of evidential partition generalizes other soft clustering structures such as fuzzy, possibilistic, or rough partitions. In this paper, we propose two extensions of the Rand index for evaluating and comparing evidential partitions, called similarity and consistency indices. The similarity index is suitable for measuring the closeness of two soft partitions, whereas the consistency index allows one to assess the agreement, or lack of conflict, between a soft partition and the true hard partition. Simulation experiments illustrate some applications of these indices.
Keyword ：
Belief functions Belief functions clustering clustering evidence theory evidence theory cluster validity measure cluster validity measure
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| GB/T 7714 | Denoeux, Thierry , Li, Shoumei , Sriboonchitta, Songsak . Evaluating and Comparing Soft Partitions: An Approach Based on Dempster-Shafer Theory [J]. | IEEE TRANSACTIONS ON FUZZY SYSTEMS , 2018 , 26 (3) : 1231-1244 . |
| MLA | Denoeux, Thierry et al. "Evaluating and Comparing Soft Partitions: An Approach Based on Dempster-Shafer Theory" . | IEEE TRANSACTIONS ON FUZZY SYSTEMS 26 . 3 (2018) : 1231-1244 . |
| APA | Denoeux, Thierry , Li, Shoumei , Sriboonchitta, Songsak . Evaluating and Comparing Soft Partitions: An Approach Based on Dempster-Shafer Theory . | IEEE TRANSACTIONS ON FUZZY SYSTEMS , 2018 , 26 (3) , 1231-1244 . |
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