Asymptotic Properties of Deep Quantile Regression Estimator for Change Point Detection

This article presents an analytical framework that utilizes deep neural network-based quantile regression to detect structural changes in high-dimensional, time dependent data. By leveraging on deep neural networks for quantile regression, the model combines the robustness of quantile regression with the computational efficiency of deep learning to estimate conditional quantiles. These estimators can identify abrupt shifts in data distribution without imposing strict structural assumptions, making them more resilient to heavy-tailed data compared to mean-based methods. The study derives the asymptotic properties of the deep quantile regression estimator for change point detection, particularly within high-dimensional, non-linear, and complex datasets. Under specific regularity conditions, the asymptotic properties of the proposed estimator are established. The simulation results demonstrate the convergence of the deep quantile regression estimator to the true conditional quantile function as the sample size. The deep quantile regression estimator achieves the minimax optimal convergence rate, effectively alleviating the curse of dimensionality when the target function adheres to a compositional structure. The empirical process theory and the method of sieve estimation are employed to demonstrate the consistency of the deep quantile regression estimator. The results show that the normalized estimator is asymptotically normal and exhibits inherent robustness to outliers and heavy-tailed noise compared to least-squares-based deep learning models. This theoretical framework provides a foundation for the construction of confidence intervals and hypothesis testing for complex, non-parametric quantile models in fields such as finance, risk management, and econometrics.