Multivariate nonlinear least squares: robustness and efficiency of standard versus Beauchamp and Cornell methodologies

Renato Guseo and Cinzia Mortarino ()

Computational Statistics, 2014, vol. 29, issue 6, 1609-1636

Abstract: 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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Nonlinear regression; Beauchamp and Cornell methodology; Robustness (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00180-014-0509-y

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