Bootstrap methods for bias correction and confidence interval estimation for nonlinear quantile regression of longitudinal data

Abstract

This paper examines the use of bootstrapping for bias correction and calculation of confidence intervals (CIs) for a weighted nonlinear quantile regression estimator adjusted to the case of longitudinal data. Different weights and types of CIs are used and compared by computer simulation using a logistic growth function and error terms following an AR(1) model. The results indicate that bias correction reduces the bias of a point estimator but fails for CI calculations. A bootstrap percentile method and a normal approximation method perform well for two weights when used without bias correction. Taking both coverage and lengths of CIs into consideration, a non-bias-corrected percentile method with an unweighted estimator performs best.

Keywords:

• autocorrelated errors
• bias reduction
• dependent errors
• median regression
• panel data
• repeated measurements

2000 Mathematics Subject Classification :

• Primary: 62F40
• 62F25
• Secondary: 62J02
• 62M10

Acknowledgements

Thanks to Dr. Johan Lyhagen, Prof. Rolf Larsson, Dr. Jonas Andersson and an anonymous referee for their valuable comments and suggestions. This work was mainly performed as a part of the author's graduate studies at the Division of Statistics, Department of Information Sciences, Uppsala University, during the years 2001–2006.