Kernel-smoothed conditional quantiles of randomly censored functional stationary ergodic data

TL;DR

This paper develops a kernel-based method for estimating conditional quantiles in functional stationary ergodic data with censorship, providing strong consistency, asymptotic normality, and practical confidence intervals, demonstrated through electricity demand data.

Contribution

Introduces a novel kernel estimator for conditional quantiles in censored functional data, with proven consistency and asymptotic normality, applicable in real-world scenarios.

Findings

Estimator is strongly consistent with a known rate.

Asymptotic normality allows for practical confidence intervals.

Application to electricity demand data demonstrates effectiveness.

Abstract

This paper, investigates the conditional quantile estimation of a scalar random response and a functional random covariate (i.e. valued in some infinite-dimensional space) whenever {\it functional stationary ergodic data with random censorship} are considered. We introduce a kernel type estimator of the conditional quantile function. We establish the strong consistency with rate of this estimator as well as the asymptotic normality which induces a confidence interval that is usable in practice since it does not depend on any unknown quantity. An application to electricity peak demand interval prediction with censored smart meter data is carried out to show the performance of the proposed estimator.