Renewable Composite Quantile Method and Algorithm for Nonparametric Models with Streaming Data

TL;DR

This paper introduces a renewable weighted composite quantile regression method for nonparametric models with streaming data, offering robustness, efficiency, and asymptotic unbiasedness, validated through simulations and real data.

Contribution

It develops a novel renewable WCQR method with optimal weight functions and practical bandwidth selectors for streaming data, improving estimation accuracy and robustness.

Findings

Estimator is nearly equivalent to the oracle estimator.

Method is robust to outliers and adaptable to error distributions.

Simulation and real data confirm theoretical advantages.

Abstract

We are interested in renewable estimations and algorithms for nonparametric models with streaming data. In our method, the nonparametric function of interest is expressed through a functional depending on a weight function and a conditional distribution function (CDF). The CDF is estimated by renewable kernel estimations combined with function interpolations, based on which we propose the method of renewable weighted composite quantile regression (WCQR). Then we fully use the model structure and obtain new selectors for the weight function, such that the WCQR can achieve asymptotic unbiasness when estimating specific functions in the model. We also propose practical bandwidth selectors for streaming data and find the optimal weight function minimizing the asymptotic variance. The asymptotical results show that our estimator is almost equivalent to the oracle estimator obtained from the entire data together. Besides, our method also enjoys adaptiveness to error distributions, robustness to outliers, and efficiency in both estimation and computation. Simulation studies and real data analyses further confirm our theoretical findings.