Quantile Regression Estimation of Nonlinear Longitudinal Data

This paper examines a weighted version of the quantile regression estimator defined by Koenker and Bassett (1978), adjusted to the case of nonlinear longitudinal data. Different weights are used and compared by computer simulation using a four-parameter logistic growth function and error terms following an AR(1) model. It is found that the estimator is performing quite well, especially for the median regression case, that the differences between the weights are small, and that increasing the correlation in the AR(1) model leads to better behaviour of the estimator. A comparison is made with the corresponding mean regression estimator, which is found to be less robust. Finally the estimator is applied to a data set with growth patterns of two genotypes of soybean. AMS (2000) subject classification. 62M10, 62G30.