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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

On Independent Reference Priors

Lee, Mi Hyun 09 January 2008 (has links)
In Bayesian inference, the choice of prior has been of great interest. Subjective priors are ideal if sufficient information on priors is available. However, in practice, we cannot collect enough information on priors. Then objective priors are a good substitute for subjective priors. In this dissertation, an independent reference prior based on a class of objective priors is examined. It is a reference prior derived by assuming that the parameters are independent. The independent reference prior introduced by Sun and Berger (1998) is extended and generalized. We provide an iterative algorithm to derive the general independent reference prior. We also propose a sufficient condition under which a closed form of the independent reference prior is derived without going through the iterations in the iterative algorithm. The independent reference prior is then shown to be useful in respect of the invariance and the first order matching property. It is proven that the independent reference prior is invariant under a type of one-to-one transformation of the parameters. It is also seen that the independent reference prior is a first order probability matching prior under a sufficient condition. We derive the independent reference priors for various examples. It is observed that they are first order matching priors and the reference priors in most of the examples. We also study an independent reference prior in some types of non-regular cases considered by Ghosal (1997). / Ph. D.
2

Estatística gradiente: teoria assintótica de alta ordem e correção tipo-Bartlett / Gradient statistic: higher order asymptotics and Bartlett-type correction

Vargas, Tiago Moreira 15 April 2013 (has links)
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. / 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.
3

Estatística gradiente: teoria assintótica de alta ordem e correção tipo-Bartlett / Gradient statistic: higher order asymptotics and Bartlett-type correction

Tiago Moreira Vargas 15 April 2013 (has links)
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. / 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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