Statistics and Its Interface

Volume 15 (2022)

Number 2

Distribution free prediction intervals for multiple functional regression

Pages: 161 – 170



Kehui Chen (University of Pittsburgh)

Ryan Kelly (University of Pittsburgh)


This paper applies conformal prediction techniques to the problem of constructing prediction intervals in a multiple functional regression setting. After a short introduction to the Signature expansion and its favorable properties, a method utilizing this feature set is developed with great modeling flexibility. With minimal assumptions, the resulting algorithm produces a closed form solution for a prediction set with guaranteed coverage. The good performance of the proposed method is illustrated using simulations and data examples.


multiple functional regression, prediction intervals, conformal prediction, signature expansion

Received 25 February 2020

Accepted 14 October 2020

Published 11 January 2022