Abstract
Resumo: Para modelos F pertencentes à classe de Hall, a função quantil U(t) é de variação regular com índice igual a Υ, onde Υ > 0 é o índice de cauda. Para x > 0, a velocidade de convergência de U(tx)/U(t)-xΥ para zero, quando t → ∞ pode ser medida através da função A(t)=ΥβtΡ , ρ < 0, β ∈ R. A estimação de ρ, o parâmetro de "forma" de segunda ordem, é um tema bastante abordado na literatura, mas pouco existe relativamente à estimação do parâmetro de "escala" de segunda ordem β . Num contexto semi-paramétrico, introduzimos uma classe de estimadores de β e provamos a sua consistência. Serão também de Monte Carlo estudamos, para amostras de dimensão finita de alguns modelos de cauda pesada, as propriedades desta classe de estimadores de β .
Abstract: In Hall's class of heavy-tailed models, the quantile function U(t) is of regular variation with an index equal to Υ, where Υ > 0 is the tail index. For every x > 0, the rate of convergence of U(tx)/U(t)-xΥ towards zero, as t → ∞ may the be measured through a function A(t)=ΥβtΡ , ρ < 0, β ∈ R. The estimation of ρ, the "shape" second order parameter, has been extensively addressed in the literature, but practically nothing has been done related to the estimation of the "scale" second order parameter β . Under a semi-parametric framework, we shall introduce a class of β - estimators and study their consistency. We shall deal with the conditions enabling us to get the asymptotic normality of this class of estimators, and we shall illustrate the behaviour of the estimators, throught Monte Carlo simulation techniques, for a wide variety of heavy-tailed models.
Abstract: In Hall's class of heavy-tailed models, the quantile function U(t) is of regular variation with an index equal to Υ, where Υ > 0 is the tail index. For every x > 0, the rate of convergence of U(tx)/U(t)-xΥ towards zero, as t → ∞ may the be measured through a function A(t)=ΥβtΡ , ρ < 0, β ∈ R. The estimation of ρ, the "shape" second order parameter, has been extensively addressed in the literature, but practically nothing has been done related to the estimation of the "scale" second order parameter β . Under a semi-parametric framework, we shall introduce a class of β - estimators and study their consistency. We shall deal with the conditions enabling us to get the asymptotic normality of this class of estimators, and we shall illustrate the behaviour of the estimators, throught Monte Carlo simulation techniques, for a wide variety of heavy-tailed models.
Original language | Portuguese |
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Title of host publication | Estatística jubilar |
Subtitle of host publication | Actas do XII Congresso Anual da Sociedade Portuguesa de Estatística |
Editors | Carlos Braumann, Paulo Infante, Manuela Oliveira, Russell Alpizar-Jara, Fernando Rosado |
Place of Publication | Lisboa |
Publisher | Sociedade Portuguesa de Estatística |
Pages | 113-124 |
Number of pages | 12 |
ISBN (Print) | 972-8890-04-4 |
Publication status | Published - 2005 |
Event | XII Congresso Anual da Sociedade Portuguesa de Estatística - Évora, Portugal Duration: 29 Sep 2004 → 2 Oct 2004 |
Conference
Conference | XII Congresso Anual da Sociedade Portuguesa de Estatística |
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Country/Territory | Portugal |
City | Évora |
Period | 29/09/04 → 2/10/04 |
Keywords
- caudas pesadas
- estimação semi-paramétrica
- parâmetros de segunda ordem
- método de Monte Carlo
- heavy tails
- semi-parametric estimation
- second order parameters
- Monte Carlo methodology