Bootstrap Confidence Intervals In Nonlinear Regression Models When The Number of Observations is Fixed and The Variance Tends To 0. Application To Biadditive Models

We consider a parametric nonlinear regression model with independent and Gaussian errors. We assume that the number of observations is fixed and that the variance of errors tends to zero; we then derive the properties of confidence intervals for the parameters. These confidence intervals are calculated using both the quantiles of the estimator's asymptotic law and the quantiles of the estimator's bootstrap distribution. We show that if the pseudo-errors are simulated using the Gaussian distribution, then bootstrap can be applied successfully. The usual reduction in coverage error of confidence intervals is not, however, verified. A simulation study for a biadditive model shows the superiority of bootstrap when calculating confidence intervals for the interaction parameters.