L. Brin, Pierre-Nicolas Clauss, François Crénin, Sophie Lavaud, Jiali Xu
{"title":"Unsupervised Learning Applied to the Grouped t-Copula or the Modeling of Real-Life Dependence","authors":"L. Brin, Pierre-Nicolas Clauss, François Crénin, Sophie Lavaud, Jiali Xu","doi":"10.2139/ssrn.3100048","DOIUrl":"https://doi.org/10.2139/ssrn.3100048","url":null,"abstract":"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).","PeriodicalId":353809,"journal":{"name":"GeologyRN: Computational Methods in Geology (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128022159","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}
{"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}
{"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
{"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}