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

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  • Renato Guseo
  • Cinzia Mortarino

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

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  • Renato Guseo & Cinzia Mortarino, 2014. "Multivariate nonlinear least squares: robustness and efficiency of standard versus Beauchamp and Cornell methodologies," Computational Statistics, Springer, vol. 29(6), pages 1609-1636, December.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1609-1636
    DOI: 10.1007/s00180-014-0509-y
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