A predictive leverage statistic for quantile regression with measurement errors

ABSTRACT

Application of quantile regression models with measurement errors in predictors is becoming increasingly popular. High leverage points in predictors can have substantial impacts on these models. Here, we propose a predictive leverage statistic for these models, assuming that the measurement errors follow a multivariate normal distribution, and derive its exact distribution. We compare its performance versus known predictive leverage statistics using simulation and a real dataset. The proposed statistic is shown to have desirable features. It is also the first predictive leverage statistic having its distribution derived in a closed form.

KEYWORDS:

• Elemental predictive leverage
• Elemental regression weight
• Elemental regression
• Elemental set
• Multiple case
• Quantile regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E99

Acknowledgments

The authors would like to thank the Editor and the two referees for careful reading and comments which greatly improved the article.