Application of nonparametric statistics to the estimation of the accuracy of Monte Carlo confidence intervals in regression analysis.

Confidence intervals and their uncertainties for nonlinear regression parameters are obtained using nonparametric statistical methods. The confidence intervals are calculated by means of a Monte Carlo procedure. Their uncertainties depend on the confidence level desired and on the number of Monte Carlo simulations of the data set. They are obtained by calculating the uncertainties in the boundaries of the confidence intervals using a generalization of the nonparametric method used to calculate confidence intervals for medians. The method described here provides reliable confidence intervals at relatively low computational expense. It seems especially suited to the statistical analysis of nonlinear regression problems that are difficult to deal with using conventional methods.