Multivariate Nonlinear Least Squares: Robustness and Efficiency of Standard versus Beauchamp and Cornell Methodologies

Simultaneous estimation in nonlinear multivariate regression contexts is a complex problem in inference. In this paper, we compare the methodology suggested in the literature for an unknown covariance matrix among response components, the methodology by Beauchamp and Cornell (B&C), with the standard nonlinear least squares approach (NLS). In the first part of the paper, we contrast B&C and the standard NLS, pointing out, from the theoretical point of view, how a model specification error could affect the estimation. A comprehensive simulation study is also performed to evaluate the effectiveness of B&C versus standard NLS under both correct and misspecified models. Several alternative models are considered to highlight the consequences of different types of specification error. An application to a real dataset within the context of quantitative marketing is presented.