A Robust Procedure in Nonlinear Models for Repeated Measurements

Abstract

Nonlinear regression models arise when definite information is available about the form of the relationship between the response and predictor variables. Such information might involve direct knowledge of the actual form of the true model or might be represented by a set of differential equations that the model must satisfy. We develop M-procedures for estimating parameters and testing hypotheses of interest about these parameters in nonlinear regression models for repeated measurement data. Under regularity conditions, the asymptotic properties of the M-procedures are presented, including the uniform linearity, normality and consistency. The computation of the M-estimators of the model parameters is performed with iterative procedures, similar to Newton–Raphson and Fisher's scoring methods. The methodology is illustrated by using a multivariate logistic regression model with real data, along with a simulation study.

Keywords:

• Consistency
• M-estimators
• M-tests
• Normality
• Uniform asymptotic linearity
• Wald-type tests

Mathematics Subject Classification:

• Primary 62J02
• Secondary 62G35

Acknowledgments

The authors wish to thank the Editor and referees for their helpful comments that aided in improving this article. This study was partially supported by DIUFRO DI08-0061, DIPUV 29-2006, and FONDECYT 1080326 grants, Chile.