L. Brin, Pierre-Nicolas Clauss, François Crénin, Sophie Lavaud, Jiali Xu
Grouped t-copulas were introduced by Embrechts et al. (1999) and Fang et al. (2002) to address the inability of Gaussian copulas to model non-linear dependencies and of t-copulas to model heterogeneous tail-dependencies. These heterogeneous tail-dependencies can be observed in many fields (finance, hydrology, meteorology). Nonetheless, the use of grouped t-copulas comes at the price of a higher number of parameters to fit, and the necessity to form a priori unknown groups which variables' tail-dependencies are the same. This paper takes up these two challenges by providing an unsupervised method based on the bootstrapped estimates of individual t-copulas to form the groups, and a procedure to fit the grouped t-copula once the groups are known by combining the four-step procedures introduced in Brin et Xu (2016) with a bootstrap on the MLE of the grouped t-copula. This methodology gives good results on simulated data sets as soon as the number of observations is large enough (above 1000).
Embrechts等人(1999)和Fang等人(2002)引入了分组t-copula，以解决高斯copula无法模拟非线性依赖关系和t-copula无法模拟异构尾依赖关系的问题。在许多领域(金融、水文学、气象学)都可以观察到这些异质性的尾部依赖性。尽管如此，使用分组t-copulas的代价是需要更多的参数来拟合，并且必须形成一个先验的未知组，其中变量的尾部依赖关系是相同的。本文通过提供基于单个t-copula的自举估计的无监督方法来形成组，以及通过将Brin et Xu(2016)中引入的四步程序与分组t-copula的MLE上的自举相结合，在已知组后拟合分组t-copula的过程来应对这两个挑战。只要观测量足够大(超过1000)，这种方法在模拟数据集上就能得到很好的结果。
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While the Fractional Brownian Motion (FBm) has very interesting properties, such as long range dependency or self-similarity, and is therefore widely exploited in telecommunication or hydrology modeling, it is not applied in mathematical finance because it is not a semi-martingale and violates thus the no arbitrage condition. We nonetheless explain the theory of stochastic integration with FBm as integrators and non stochastic integrands.
{"title":"Stochastic Integration with Respect to Fractional Brownian Motion","authors":"Joachim Yaakov Nahmani","doi":"10.2139/SSRN.2087921","DOIUrl":"https://doi.org/10.2139/SSRN.2087921","url":null,"abstract":"While the Fractional Brownian Motion (FBm) has very interesting properties, such as long range dependency or self-similarity, and is therefore widely exploited in telecommunication or hydrology modeling, it is not applied in mathematical finance because it is not a semi-martingale and violates thus the no arbitrage condition. We nonetheless explain the theory of stochastic integration with FBm as integrators and non stochastic integrands.","PeriodicalId":353809,"journal":{"name":"GeologyRN: Computational Methods in Geology (Topic)","volume":"61 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127388800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a symmetric, nonlinear eigenvalue problem arising in earthquake initiation, and we establish the existence of inflnitely many solutions. Under the efiect of an arbitrary perturbation, we prove that the number of solutions becomes greater and greater if the perturbation tends to zero with respect to a prescribed topology. Our approach is based on nonsmooth critical-point theories in the sense of De Giorgi and Degiovanni.
{"title":"Nonlinear Eigenvalue Problems Arising in Earthquake Initiation","authors":"I. Ionescu, Vicentiu D. Rădulescu","doi":"10.57262/ade/1355926811","DOIUrl":"https://doi.org/10.57262/ade/1355926811","url":null,"abstract":"We study a symmetric, nonlinear eigenvalue problem arising in earthquake initiation, and we establish the existence of inflnitely many solutions. Under the efiect of an arbitrary perturbation, we prove that the number of solutions becomes greater and greater if the perturbation tends to zero with respect to a prescribed topology. Our approach is based on nonsmooth critical-point theories in the sense of De Giorgi and Degiovanni.","PeriodicalId":353809,"journal":{"name":"GeologyRN: Computational Methods in Geology (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130331915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Fischer, S. Gopal, Petra Staufer-Steinnocher, K. Steinnocher
This paper evaluates the classification accuracy of three neural network classifiers on a satellite image-based pattern classification problem. The neural network classifiers used include two types of the Multi-Layer-Perceptron (MLP) and the Radial Basis Function Network. A normal (conventional) classifier is used as a benchmark to evaluate the performance of neural network classifiers. The satellite image consists of 2,460 pixels selected from a section (270 x 360) of a Landsat-5 TM scene from the city of Vienna and its northern surroundings. In addition to evaluation of classification accuracy, the neural classifiers are analysed for generalization capability and stability of results. Best overall results (in terms of accuracy and convergence time) are provided by the MLP-1 classifier with weight elimination. It has a small number of parameters and requires no problem-specific system of initial weight values. Its in-sample classification error is 7.87% and its out-of-sample classification error is 10.24% for the problem at hand. Four classes of simulations serve to illustrate the properties of the classifier in general and the stability of the result with respect to control parameters, and on the training time, the gradient descent control term, initial parameter conditions, and different training and testing sets.
在一个基于卫星图像的模式分类问题上，对三种神经网络分类器的分类精度进行了评价。使用的神经网络分类器包括两种类型的多层感知器(MLP)和径向基函数网络。使用常规分类器作为基准来评估神经网络分类器的性能。该卫星图像由2460像素组成，选自维也纳市及其北部地区的Landsat-5 TM场景的一部分(270 x 360)。除了评估分类精度外，还分析了神经分类器的泛化能力和结果的稳定性。采用消权的MLP-1分类器提供了最佳的总体结果(在准确性和收敛时间方面)。它有少量的参数，不需要特定于问题的初始权重值系统。对于该问题，样本内分类误差为7.87%，样本外分类误差为10.24%。四类仿真说明了分类器的总体特性和结果在控制参数、训练时间、梯度下降控制项、初始参数条件以及不同训练和测试集方面的稳定性。
{"title":"Evaluation of Neural Pattern Classifiers for a Remote Sensing Application","authors":"M. Fischer, S. Gopal, Petra Staufer-Steinnocher, K. Steinnocher","doi":"10.2139/ssrn.1523788","DOIUrl":"https://doi.org/10.2139/ssrn.1523788","url":null,"abstract":"This paper evaluates the classification accuracy of three neural network classifiers on a satellite image-based pattern classification problem. The neural network classifiers used include two types of the Multi-Layer-Perceptron (MLP) and the Radial Basis Function Network. A normal (conventional) classifier is used as a benchmark to evaluate the performance of neural network classifiers. The satellite image consists of 2,460 pixels selected from a section (270 x 360) of a Landsat-5 TM scene from the city of Vienna and its northern surroundings. In addition to evaluation of classification accuracy, the neural classifiers are analysed for generalization capability and stability of results. Best overall results (in terms of accuracy and convergence time) are provided by the MLP-1 classifier with weight elimination. It has a small number of parameters and requires no problem-specific system of initial weight values. Its in-sample classification error is 7.87% and its out-of-sample classification error is 10.24% for the problem at hand. Four classes of simulations serve to illustrate the properties of the classifier in general and the stability of the result with respect to control parameters, and on the training time, the gradient descent control term, initial parameter conditions, and different training and testing sets.","PeriodicalId":353809,"journal":{"name":"GeologyRN: Computational Methods in Geology (Topic)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129453049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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