Inference on linear quantile regression with dyadic data

Abstract

This paper focuses on developing a robust inference procedure for the linear quantile regression estimator in the context of dyadic data structures. We investigate the asymptotic distribution of the quantile regression estimator under dependency structures arising from shared nodes in both undirected and directed networks. We establish consistency results for the covariance matrix estimator and provide asymptotic distributions for the associated $t$-statistic and Wald statistic, particularly in both univariate and joint hypothesis testing scenarios. To showcase the effectiveness of our proposed method, we present numerical simulations and an empirical application using international trade data. Our results demonstrate the excellent performance of the robust $t$-statistic and Wald statistic in quantile regression inference with dyadic data.