Thèse de Doctorat
DOI
10.11606/T.45.2012.tde-15082012-093632
Document
Auteur
Nom complet
Jalmar Manuel Farfan Carrasco
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Paulo, 2012
Directeur
Jury
Ferrari, Silvia Lopes de Paula (Président)
Martinez, Raydonal Ospina
Moura, Fernando Antônio da Silva
Valle, Reinaldo Boris Arellano
Titre en portugais
Modelos de regressão beta com erro nas variáveis
Mots-clés en portugais
análise de diagnóstico.
calibração da regressão
modelo com erros de medida
Modelo de regressão beta
Resumé en portugais
Titre en anglais
Beta regression model with measurement error
Mots-clés en anglais
Beta regression model
diagnostic analysis.
maximum likelihood estimation
measurement error model
pseudo-maximum likelihood estimation
regression calibration
Resumé en anglais
In this thesis, we propose a beta regression model with measurement error. Among nonlinear models with measurement error, such a model has not been studied extensively. Here, we discuss estimation methods such as maximum likelihood, pseudo-maximum likelihood, and regression calibration methods. The maximum likelihood method estimates parameters by directly maximizing the logarithm of the likelihood function. The pseudo-maximum likelihood method is used when the inference in a given model involves only some but not all parameters. Hence, we say that the model under study presents parameters of interest, as well as nuisance parameters. When we replace the true covariate (observed variable) with conditional estimates of the unobserved variable given the observed variable, the method is known as regression calibration. We compare the aforementioned estimation methods through a Monte Carlo simulation study. This simulation study shows that maximum likelihood and pseudo-maximum likelihood methods perform better than the calibration regression method and the naïve approach. We use the programming language Ox (Doornik, 2011) as a computational tool. We calculate the asymptotic distribution of estimators in order to calculate confidence intervals and test hypotheses, as proposed by Carroll et. al (2006, Section A.6.6), Guolo (2011) and Gong and Samaniego (1981). Moreover, we use the likelihood ratio and gradient statistics to test hypotheses. We carry out a simulation study to evaluate the performance of the likelihood ratio and gradient tests. We develop diagnostic tests for the beta regression model with measurement error. We propose weighted standardized residuals as defined by Espinheira (2008) to verify the assumptions made for the model and to detect outliers. The measures of global influence, such as the generalized Cook's distance and likelihood distance, are used to detect influential points. In addition, we use the conformal approach for evaluating local influence for three perturbation schemes: case-weight perturbation, respose variable perturbation, and perturbation in the covariate with and without measurement error. We apply our results to two sets of real data to illustrate the theory developed. Finally, we present our conclusions and possible future work.

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teseJalmar.pdf (1.34 Mbytes)
Date de Publication
2012-08-23

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