Extreme value inference for quantile regression with varying coefficients

Quantile regression at the tail, the estimation of which is challenging because of data sparsity, is of interest in several fields such as financial cost calculations, rainfall prediction, and environmental risk assessment. In linear models, the tail behavior of a quantile regression estimator is well developed. However, for some data, a linear model is unrealistic at the tail, requiring us to use a more flexible model. In this regard, we focus on using models with varying coefficients. Thus, the study presented in this paper is concerned with extremal quantile regression based on models with a varying coefficient.