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Spatial Expectile Predictions for Elliptical Random Fields

  • V. Maume-Deschamps
  • D. Rullière
  • A. Usseglio-Carleve
Article

Abstract

In this work, we consider an elliptical random field. We propose some spatial expectile predictions at one site given observations of the field at some other locations. To this aim, we first give exact expressions for conditional expectiles, and discuss problems that occur for computing these values. A first affine expectile regression predictor is detailed, an explicit iterative algorithm is obtained, and its distribution is given. Direct simple expressions are derived for some particular elliptical random fields. The performance of this expectile regression is shown to be very poor for extremal expectile levels, so that a second predictor is proposed. We prove that this new extremal prediction is asymptotically equivalent to the true conditional expectile. We also provide some numerical illustrations, and conclude that Expectile Regression may perform poorly when one leaves the Gaussian random field setting.

Keywords

Elliptical distribution Expectile regression Extremal expectile Spatial prediction Kriging 

Mathematics Subject Classification (2010)

60G15 60G60 62H11 62M30 

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Notes

Acknowledgments

The authors thank the referee for his comments and suggestions that really helped to improve the paper. We are also grateful to the Editor-in-Chief, Joseph Glaz, for cordial exchanges. This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • V. Maume-Deschamps
    • 1
  • D. Rullière
    • 2
  • A. Usseglio-Carleve
    • 1
  1. 1.Institut Camille Jordan ICJ UMR 5208 CNRSUniversité de Lyon, Université Lyon 1VilleurbanneFrance
  2. 2.Laboratoire SAF EA2429Université de Lyon, Université Lyon 1VilleurbanneFrance

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