Tesis
Inferência em modelos de regressão com erros de medição sob enfoque estrutural para observações replicadas
Date
2014-03-10Registration in:
TOMAYA, Lorena Yanet Cáceres. Inferência em modelos de regressão com erros de medição sob enfoque estrutural para observações replicadas. 2014. 92 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2014.
Author
Tomaya, Lorena Yanet Cáceres
Institutions
Abstract
The usual regression model fits data under the assumption that the explanatory variable is measured without error. However, in many situations the explanatory variable is observed with measurement errors. In these cases, measurement error models are recommended. We study a structural measurement error model for replicated observations. Estimation of parameters of the proposed models was obtained by the maximum likelihood and maximum pseudolikelihood methods. The behavior of the estimators was assessed in a simulation study with different numbers of replicates. Moreover, we proposed the likelihood ratio test, Wald test, score test, gradient test, Neyman's C test and pseudolikelihood ratio test in order to test hypotheses of interest related to the parameters. The proposed test statistics are assessed through a simulation study. Finally, the model was fitted to a real data set comprising measurements of concentrations of chemical elements in samples of Egyptian pottery. The computational implementation was developed in R language.