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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2017.tde-12052017-103436
Document
Author
Full name
Fabiana Uchôa Barros
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Botter, Denise Aparecida (President)
Barroso, Lucia Pereira
Cysneiros, Audrey Helen Mariz de Aquino
Opazo, Miguel Angel Uribe
Vasconcellos, Klaus Leite Pinto
 
Title in Portuguese
Refinamentos assintóticos em modelos lineares generalizados heteroscedáticos
Keywords in Portuguese
Coeficiente de assimetria
Coeficiente de curtose
Correção tipo-Bartlett
Estimadores de máxima verossimilhança
Matriz de covariâncias de segunda ordem
Abstract in Portuguese
Nesta tese, desenvolvemos refinamentos assintóticos em modelos lineares generalizados heteroscedásticos (Smyth, 1989). Inicialmente, obtemos a matriz de covariâncias de segunda ordem dos estimadores de máxima verossimilhança corrigidos pelos viés de primeira ordem. Com base na matriz obtida, sugerimos modificações na estatística de Wald. Posteriormente, derivamos os coeficientes do fator de correção tipo-Bartlett para a estatística do teste gradiente. Em seguida, obtemos o coeficiente de assimetria assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Finalmente, exibimos o coeficiente de curtose assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Analisamos os resultados obtidos através de estudos de simulação de Monte Carlo.
 
Title in English
Asymptotic refinements in heteroskedastic generalized linear models
Keywords in English
Asymptotic skewnes
Bartlett-type correction
Heteroskedastic generalized linear models
Maximum likelihood estimators
Second-order covariance matrix
Abstract in English
In this thesis, we have developed asymptotic refinements in heteroskedastic generalized linear models (Smyth, 1989). Initially, we obtain the second-order covariance matrix for the maximum likelihood estimators corrected by the bias of first-order. Based on the obtained matrix, we suggest changes in Wald statistics. In addition, we derive the coeficients of the Bartlett-type correction factor for the statistical gradient test. After, we get asymptotic skewness of the distribution of the maximum likelihood estimators of the model parameters. Finally, we show the asymptotic kurtosis coeficient of the distribution of the maximum likelihood estimators of the model parameters. Monte Carlo simulation studies are developed to evaluate the results obtained.
 
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Publishing Date
2017-05-25
 
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