Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data

Abstract

In this paper, we propose nonlinear elliptical models for correlated data with heteroscedastic and/or autoregressive structures. Our aim is to extend the models proposed by Russo et al. 22 by considering a more sophisticated scale structure to deal with variations in data dispersion and/or a possible autocorrelation among measurements taken throughout the same experimental unit. Moreover, to avoid the possible influence of outlying observations or to take into account the non-normal symmetric tails of the data, we assume elliptical contours for the joint distribution of random effects and errors, which allows us to attribute different weights to the observations. We propose an iterative algorithm to obtain the maximum-likelihood estimates for the parameters and derive the local influence curvatures for some specific perturbation schemes. The motivation for this work comes from a pharmacokinetic indomethacin data set, which was analysed previously by Bocheng and Xuping 1 under normality.

Keywords:

• autoregressive structure
• correlated data
• elliptical distributions
• heteroscedastic models
• nonlinear models

Acknowledgements

The authors are grateful to FAPESP, FACEPE and CNPq, Brazil, which supported this research.