Bootstrap-based inferential improvements to the simplex nonlinear regression model

Alisson de Oliveira Silva; Jonas Weverson de Ararújo Silva; Patrícia L Espinheira

doi:10.1371/journal.pone.0272512

Bootstrap-based inferential improvements to the simplex nonlinear regression model

PLoS One. 2022 Aug 9;17(8):e0272512. doi: 10.1371/journal.pone.0272512. eCollection 2022.

Authors

Alisson de Oliveira Silva¹, Jonas Weverson de Ararújo Silva², Patrícia L Espinheira³

Affiliations

¹ Instituto Federal de Educação, Ciência e Tecnologia da Paraíba, João Pessoa, Brazil.
² Centro de Ciências Agrárias, Departamento de Ciências Fundamentais e Sociais, Areia, Paraíba, Brazil.
³ Departamento de Estatística, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil.

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Nonlinear Dynamics*

Grants and funding

During her doctoral work, Jonas Weverson de Araújo Silva received a scholarship of approximately $423 (four hundred and twenty-three dollars) per month just to cover her living and food expenses. This scholarship is provided to the student by a federal agency in Brazil called “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES”. The authors have no grant of any kind.