Bootstrap-based inferential improvements to the simplex nonlinear regression model

Abstract

In this paper we evaluate the performance of point and interval estimators based on the maximum likelihood(ML) method for the nonlinear simplex regression model. Inferences based on traditional maximum likelihood estimation have good asymptotic properties, but their performance in small samples may not be satisfactory. At out set we consider the maximum likelihood estimation for the parameters of the nonlinear simplex regression model, and so we introduced a bootstrap-based correction for such estimators of this model. We also develop the percentile and bootstrapt confidence intervals for those parameters as competitors to the traditional approximate confidence interval based on the asymptotic normality of the maximum likelihood estimators (MLEs). We then numerically evaluate the performance of these different methods for estimating the simplex regression model. The numerical evidence favors inference based on the bootstrap method, in special the bootstrapt interval, which was decisive in an application to real data.