Estimation in quantile regression models for correlated data with diverging number of covariates and large cluster sizes

Abstract

In many data analytic problems, repeated measurements with a large number of covariates are collected and conditional quantile modeling for such correlated data are often of significant interest, especially in medical applications. We propose a quadratic inference functions based approach to take into account the correlations within clusters and use smoothing to make the objective function amenable to computation. We show that the asymptotic properties of the estimators are the same whether or not smoothing is applied, established in the “diverging p, large n” setting. The cluster sizes are also allowed to diverge with sample size n. Simulation results are presented to demonstrate the effectiveness of the proposed estimator by taking into account the within-cluster correlations and we use a longitudinal data set to illustrate the method.

Keywords:

• Clustered data
• diverging dimensionality
• induced smoothing
• quadratic inference functions
• quantile regression

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62F10

Acknowledgements

The authors sincerely thank the anonymous reviewers for their insightful comments that greatly improved the paper.

Additional information

Funding

The research of Rui Li was supported by National Social Science Fund of China (No. 17BTJ025).