Bias Correction in Nonlinear Regression via Two-Stages Least-Squares Estimation

Abstract A two-stages least-squares approach is suggested for bias reduction in nonlinear parameter estimation (with a reduction of the mean-squared error often obtained as a by-product). While the classical use of Box formula for bias-correction frequently leads to unsatisfactory results, the new approach seems promissing. It does not require the computation of derivatives of the model response. It can thus be of special interest when the value of the response is not known analytically and can only be obtained as the numerical solution of a differential equation. Various illustrative examples are considered.