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A Conformal Approach for Distribution-free Prediction of Functional Data

  • Matteo FontanaEmail author
  • Simone Vantini
  • Massimo Tavoni
  • Alexander Gammerman
Conference paper
  • 138 Downloads
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Interval prediction has always been a complex problem to solve in the realm of Functional Data Analysis, and the solutions currently proposed to address this very important theoretical and applied issue are not satisfactory. In this contribution we propose a novel approach, based on a non-parametric forecasting approach coming from machine learning, called Conformal Prediction. In the scalar setting, the method is based on simple yet remarkable considerations about sample quantiles. After having stated in a formal way the issue of forecasting for functional data, we develop an algorithm that can be used to generate non-parametric prediction bands for a functional-on-scalar linear regression model. These forecasts are proven to be valid in a statistical sense (i.e., they guarantee a global coverage probability larger or equal to a given threshold) under a very minimal set of assumptions, and thus extremely useful in the statistical practice. The method is then tested on a realworld application, namely ensemble emulations for climate economy models, very used in the climate change economics realm.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Matteo Fontana
    • 1
    Email author
  • Simone Vantini
    • 1
  • Massimo Tavoni
    • 2
    • 3
  • Alexander Gammerman
    • 4
  1. 1.MOX - Department of MathematicsPolitecnico di MilanoMilanItaly
  2. 2.Department of Management, Economics and Industrial EngineeringPolitecnico di MilanoMilanItaly
  3. 3.RFF-CMCC European Institute on Economics and the Environment (EIEE)Fondazione CMCCLecceItaly
  4. 4.Computer Learning Research Center - Department of Computer Science, Royal HollowayUniversity of LondonLondonUK

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