Some simulations results about confidence intervals and bootstrap methods in nonlinear regression

Abstract

A simulation study has been carried out in order to compare different methods for calculating approximate confidence intervals for parameters in nonlinear regression, when the number of observations is small. We are particularly interested in methods for which it is possible to appreciate (asymptotically) the degree of approximation. In fact, two types of approach to the problem can be distinguished. The first one is based on the estimate's asymptotic law which can be calculated using Edgeworth expansions, the second one is based on resampling methods, such as bootstrap. For the different models considered in this simulation study, it appears that the first order asymptotic method gives the best result when the estimator is nearly normally distributed, the second order asymptotic must be used very cautiously, the bootstrap method gives quite good results for disturbed {biased and far from a Gaussian) estimators.

Keywords:

• Nonlinear regression confidence intervals
• Edgeworth expansions
• reparame-trization
• likelihood contours
• jackknife
• bootstrap