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Doctoral Thesis
DOI
10.11606/T.45.2008.tde-30102008-000235
Document
Author
Full name
Flavio Henn Ferreira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Kolev, Nikolai Valtchev (President)
Balakrishnan, Narayanaswamy
Belitsky, Vladimir
Fernandes, Cristiano Augusto Coelho
Mendes, Beatriz Vaz de Melo
Title in Portuguese
Medidas de assimetria bivariada e dependência local.
Keywords in Portuguese
associatividade
bi-simetria
coeficiente de correlação condicional
dependência local
permutabilidade
quantil bivariado
simetria radial
Abstract in Portuguese
Esta tese trata de dois assuntos importantes na teoria de risco: o fenômeno da dependência local e a identificação e mensuração de assimetrias apresentadas pelos dados. A primeira parte trata de dependência local, sendo abordadas algumas medidas já analisadas na literatura. Versões locais dos coeficientes de Kendall e Spearman , baseadas na distribuição condicional dos dados, são propostas. São apresentadas algumas propriedades dessas medidas e a aplicação das mesmas a algumas cópulas. Na segunda parte são apresentados resultados sobre cópulas bivariadas que são as menos associativas e menos bi-simétricas segundo o critério de máxima distância modular. A última parte trata da não-permutabilidade e assimetria radial dos dados. Uma medida de não-permutabilidade baseada nos coeficientes de correlação condicional é proposta e aplicada a algumas distribuições. No final, o conceito de quantil bivariado é aplicado nas definições de medidas para avaliar o grau de permutabilidade e de simetria radial presentes na estrutura de dependência dos dados e de testes de hipóteses para verificar se a cópula subjacente aos dados é permutável ou radialmente simétrica.
Title in English
Measures of bivariate asymmetry and local dependence.
Keywords in English
associativity
bi-symmetry
bivariate quantile
conditional correlation coefficient
exchangeability
local dependence
radial symmetry.
Abstract in English
In this thesis two important fields in risk theory are studied: the local dependence phenomenon and the identification and measuring of asymmetries contained in data. The first part deals with local dependence: some measures already studied in the literature are presented and discussed, and local versions of the coefficients Kendall and Spearman , based on the conditional distribution of data, are proposed. Properties of these measures and some examples concerning its application are treated. In the second part are presented some results about bivariate copulas which are the least associative and the least bi-symmetric according to the maximum modular distance. The last part analyses the nonexchangeability and the radial asymmetry of data. A measure of nonexchangeability based on the conditional correlation coefficient is proposed and applied to some distribution functions. At the end, the concept of bivariate quantile is applied in the definitions of measures for evaluating the degree of exchangeability and radial symmetry present in data and of hypothesis tests proposed for verifying whether the underlying copula is exchangeable or radially symmetric.
 
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Publishing Date
2008-12-11
 
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