Randomly censored quantile regression estimation using functional stationary ergodic data

Abstract

This paper investigates the conditional quantile estimation of a randomly censored scalar response variable given a functional random covariate (i.e. valued in some infinite-dimensional space) whenever a stationary ergodic data are considered. A kernel-type estimator of the conditional quantile function is introduced. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under mild assumptions. A simulation study is considered to show the performance of the proposed estimator. An application to the electricity peak demand prediction using censored smart meter data is also provided.

Keywords:

• asymptotic normality
• censored data
• conditional quantile
• ergodic processes
• functional data
• peak load forecasting
• strong consistency

AMS Subject Classification::

• 62G20
• 62N01
• 62P30
• 62M10

Acknowledgements

The authors would like to thank the Editor and two anonymous reviewers for their valuable comments which improved substantially the quality of an earlier version of this paper.

Funding

The first author thanks the Scottish and Southern Power Distribution SSEPD for their support and funding via the New Thames Valley Vision Project [SSET203 – New Thames Valley Vision] funded through the Low Carbon Network Fund.