Tesis Doctoral
DOI
10.11606/T.11.2011.tde-13092011-095857
Documento
Autor
Nombre completo
Lucimary Afonso dos Santos
Dirección Electrónica
Área de Conocimiento
Fecha de Defensa
Publicación
Piracicaba, 2011
Director
Tribunal
Demetrio, Clarice Garcia Borges (Presidente)
Barbin, Decio
Cordeiro, Gauss Moutinho
Costa, Silvano Cesar da
Silveira, Liciana Vaz de Arruda
Título en portugués
Modelos de regressão simplex: resíduos de Pearson corrigidos e aplicações
Palabras clave en portugués
Modelos matemáticos
Regressão linear.
Resíduos
Resumen en portugués
Título en inglés
Simplex regression models:corrected Pearson residuals and applications
Palabras clave en inglés
Distributions (Probability)
Linear Regression.
Mathematical Models
Residuals
Statistical Data Analysis
Resumen en inglés
The simplex distribution, proposed by Barndor-Nielsen e Jørgensen (1991) is useful for modeling continuous data in the (0,1) interval. In this work, we developed the simplex regression model, considering ´ = h(X; ¯), where h(:; :) is an arbitrary function. We dened the residuals to this model and obtained asymptotic corrections to residuals of the type Ri. The rst correction proposed, was based in obtaining the asymptotic expression for the density of Pearson residuals, corrected to order O(n¡1). These residuals were dened in order to have the same distribution of true Pearson residuals. Simulation studies showed that the empirical distribution of the modied residuals is closer to the distribution of the true Pearson residuals than the unmodied Pearson residuals. The second one, considers the method of moments. Generally E(Ri) and Var(Ri) are dierent from zero and one, respectively, by terms of order O(n¡1). Using the results of Cox and Snell (1968), we obtained the approximate expressions of order O(n¡1) for E(Ri) and Var(Ri). A simulation study is being conducted to evaluate the proposed technique. We applied the techniques in two data sets, the rst one, is a dataset of ammonia oxidation, considering linear predictor and the other one was the percentage of dry matter in maize, considering linear predictor and nonlinear. The results obtained for the oxidation ammonia data indicated that the model considering linear predictor, tted well to the data, if we consider the exclusion of some possible inuential points. The proposed correction for the density of Pearson residuals, showed better results. Observing the results for the dry matter data, the best results were obtained for a model with a specied nonlinear predictor.

ADVERTENCIA - La consulta de este documento queda condicionada a la aceptación de las siguientes condiciones de uso:
Este documento es únicamente para usos privados enmarcados en actividades de investigación y docencia. No se autoriza su reproducción con finalidades de lucro. Esta reserva de derechos afecta tanto los datos del documento como a sus contenidos. En la utilización o cita de partes del documento es obligado indicar el nombre de la persona autora.
errata_Lucimary.pdf (54.23 Kbytes)
Fecha de Publicación
2011-09-21