A robust procedure in nonlinear models for repeated measurements

Antonio Sanhueza, Pranab K. Sen, VICTOR ELISEO LEIVA SANCHEZ

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish
Pages (from-to)138-155
Number of pages18
JournalCommunications in Statistics - Theory and Methods
Volume38
Issue number1
DOIs
StatePublished - 1 Jan 2009

Keywords

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

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