Multivariate Nonlinear Least Squares: Direct and Beauchamp and Cornell Methodologies

Simultaneous estimation in nonlinear multivariate regression contexts is a complex problem in inference. In this paper, we compare the generalized least squares approach, GLS, with the well-known methodology by Beauchamp and Cornell, B&C, and with the standard nonlinear least squares approach, NLS. In the first part of the paper, we contrast B&C and standard NLS, highlighting, from the theoretical point of view, how a model specification error could affect the estimation. A comprehensive simulation study is also performed in order to evaluate the effectiveness of B&C versus standard NLS under both correct and misspecified models.