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Bootstrap-based inferential improvements to the simplex nonlinear regression model.
Alisson de Oliveira Silva1, Jonas Weverson de Ararújo Silva2, Patrícia L Espinheira3
1Instituto Federal de Educação, Ciência e Tecnologia da Paraíba, João Pessoa, Brazil.
Maximum likelihood estimation (MLE) for nonlinear simplex regression models can be unreliable in small samples. Bootstrap methods, particularly bootstrap intervals, offer improved accuracy for parameter estimation and inference in these models.
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Area of Science:
- Statistics
- Econometrics
- Biostatistics
Background:
- Traditional maximum likelihood estimation (MLE) offers asymptotic properties but can be inadequate for small sample sizes in nonlinear regression.
- The nonlinear simplex regression model presents unique challenges for accurate parameter estimation and inference.
Purpose of the Study:
- To evaluate the performance of point and interval estimators for the nonlinear simplex regression model.
- To introduce bootstrap-based corrections to enhance maximum likelihood estimators (MLEs).
- To compare traditional confidence intervals with bootstrap and percentile confidence intervals.
Main Methods:
- Maximum Likelihood Estimation (MLE) for nonlinear simplex regression.
- Development of bootstrap-based corrections for MLEs.
- Construction of percentile and bootstrap confidence intervals.
- Numerical evaluation of estimator performance.
Main Results:
- Traditional MLE performance is suboptimal in small samples.
- Bootstrap-corrected estimators demonstrate superior performance.
- Bootstrap confidence intervals show enhanced accuracy and reliability.
- The bootstrap method proved decisive in a real-data application.
Conclusions:
- Bootstrap methods, especially bootstrap intervals, are recommended for parameter estimation in nonlinear simplex regression.
- The proposed bootstrap approach improves inference accuracy over traditional methods.
- The findings have implications for statistical modeling in various scientific fields.