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Quantile predictions for elliptical random fields

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

Abstract

In this article, we consider elliptical random fields. We propose some quantile predictions at one site, given observations at some other locations. To this end, we first give exact expressions for conditional quantiles, and discuss problems that occur when computing these values. A first affine regression quantile predictor is presented in detail, an explicit formula is obtained, and its distribution is given. Direct simple expressions are derived for some particular elliptical random fields. As the performance of this regression quantile turns out to be very poor for extremal quantile levels, a second predictor is proposed. We prove that this new extremal predictor is asymptotically equivalent to the true conditional quantile. Through numerical illustrations, we show that quantile regression may perform poorly outside the usual Gaussian random field setting. This justifies the use of the proposed extremal quantile predictions.

Suggested Citation

  • Maume-Deschamps, V. & Rullière, D. & Usseglio-Carleve, A., 2017. "Quantile predictions for elliptical random fields," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 1-17.
    • Handle: RePEc:eee:jmvana:v:159:y:2017:i:c:p:1-17
    DOI: 10.1016/j.jmva.2017.04.007
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    References listed on IDEAS

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    1. Jinguo Gong & Yadong Li & Liang Peng & Qiwei Yao, 2015. "Estimation of extreme quantiles for functions of dependent random variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(5), pages 1001-1024, November.
    2. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
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    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
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    1. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.

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