Doctoral Thesis
DOI
10.11606/T.11.2011.tde-13092011-095857
Document
Author
Full name
Lucimary Afonso dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 2011
Supervisor
Committee
Demetrio, Clarice Garcia Borges (President)
Barbin, Decio
Cordeiro, Gauss Moutinho
Costa, Silvano Cesar da
Silveira, Liciana Vaz de Arruda
Title in Portuguese
Modelos de regressão simplex: resíduos de Pearson corrigidos e aplicações
Keywords in Portuguese
Modelos matemáticos
Regressão linear.
Resíduos
Abstract in Portuguese
Title in English
Simplex regression models:corrected Pearson residuals and applications
Keywords in English
Distributions (Probability)
Linear Regression.
Mathematical Models
Residuals
Statistical Data Analysis
Abstract in English
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.