A Cox-Based Framework for Quantile Estimation

Abstract

Quantile regression (QR) provides a flexible framework for characterizing conditional distributions and can offer useful insights for quantile estimation. In this paper, we provide intuition for the interpretation of QR by highlighting the approach that it is a reparameterization of more popular conditional cumulative distribution function regression. From this approach, we naturally explore the use of the proportional hazards Cox regression model in the QR context. Therefore, we propose a framework based on the Cox regression model for estimating conditional quantiles, obtained through a reparameterization of the conditional cumulative distribution function under a proportional hazards structure. We establish the large-sample properties of the resulting estimator and investigate its behavior in finite samples through a Monte Carlo simulation study. An empirical application illustrates its practical implementation in a real-world context. Furthermore, we introduce the average quantile effect, a summary measure for quantifying the effects of covariates across conditional quantiles. The proposed estimator behaves adequately under the required assumptions, although inferences on the associated parameters strongly depend on these premises.