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Doctoral Thesis
DOI
10.11606/T.45.2013.tde-13062013-163845
Document
Author
Full name
Tiago Moreira Vargas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Ferrari, Silvia Lopes de Paula (President)
Botter, Denise Aparecida
Lemonte, Artur José
Opazo, Miguel Angel Uribe
Vasconcellos, Klaus Leite Pinto
Title in Portuguese
Estatística gradiente: teoria assintótica de alta ordem e correção tipo-Bartlett
Keywords in Portuguese
Argumento de encolhimento
Correção tipo-Bartlett
Expansão assintótica
Matchingpriors
Rota Bayesiana
Teste gradiente.
Abstract in Portuguese
Obtemos uma expansão assintótica da função de distribuição sob a hipótese nula da estatística gradiente para testar hipóteses nulas compostas na presença de parâmetros de perturbação. Esta expansão é derivada utilizando uma rota Bayesiana baseada no argumento de encolhimento descrito em Ghosh e Mukerjee (1991). Usando essa expansão, propomos uma estatística gradiente corrigida por um fator de correção tipo-Bartlett, que tem distribuição qui-quadrado até um erro de ordem o(n-1) sob a hipótese nula. A partir disso, determinamos fórmulas matriciais e algébricas que auxiliam na obtenção da estatística gradiente corrigida em modelos lineares generalizados com dispersão conhecida e desconhecida. Simulações de Monte Carlo são apresentadas. Finalmente, discutimos a obtenção de regiões de credibilidade via inversão da estatística gradiente. Caracterizamos as densidades a priori, matching priors, que asseguram propriedades de cobertura frequentista acuradas para essas regiões.
Title in English
Gradient statistic: higher order asymptotics and Bartlett-type correction
Keywords in English
Asymptotic expansion
Bartlett-type correction
Bayesian route
Gradient test
Matching priors
Shrinkage argument.
Abstract in English
We obtain an asymptotic expansion for the null distribution function of the gradient statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the shrinkage argument described in Ghosh and Mukerjee (1991). Using this expansion, we propose a Bartlett-type corrected gradient statistic, which has a chi-square distribution up to an error of order o(n1) under the null hypothesis. Also, we determined matrix and algebraic formulas that assist in obtaining Bartett-type corrected statistic in generalized linear models with known and unknown dispersion. Monte Carlo simulations are presented. Finally, we obtain credible regions based by the inversion of gradient statistic. We characterize priori densities, matching priors, that ensure accurate frequentist coverage properties for these regions.
 
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TeseFinal_Tiago.pdf (443.10 Kbytes)
Publishing Date
2013-06-26
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • VARGAS, TIAGO M., FERRARI, SILVIA L P, and LEMONTE, ARTUR J. Gradient statistic: Higher-order asymptotics and Bartlett-type correction. ELECTRON J STAT [online], 2013, vol. 7, p. 43-61. [cited 2013-08-04]. Available from : <http://projecteuclid.org/euclid.ejs/1357913281>
All rights of the thesis/dissertation are from the authors
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