Bootstrap method and the modified method based on weighted sampling for nonlinear model precision estimation

The Bootstrap resampling method is introduced to the nonlinear theory for solving the precision estimation in this paper. By resampling the original sample observation data or the residuals of the dependent variable to obtain Bootstrap samples instead of the complex derivative calculations, the complete algorithms of Bootstrap method for solving the problem of nonlinear accuracy evaluation are given. Aiming at the equal probability resampling of model stochastic variable, this paper obtains the empirical distribution function of the stochastic variable in the sampling process, proposes the weighted sampling strategy, and gives the detailed calculation steps of the improved method for the accuracy evaluation. The results of experiments show that the Bootstrap method based on the resampling observations and the Bootstrap method based on the resampling residuals have stronger applicability, and can obtain more reasonable parameter standard deviations than the approximate function method and Jackknife method. Furthermore, the weighted resampling Bootstrap method based on the resampling observations and the weighted resampling Bootstrap method based on the resampling residuals can obtain more accurate precision information with extensive advantages. Those which verified the feasibility and effectiveness of using Bootstrap method and the improved algorithms proposed in this paper for precision estimation of nonlinear adjustment.