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Nonparametric inference for extremal conditional quantiles

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  • Daisuke Kurisu
  • Taisuke Otsu

Abstract

This paper studies asymptotic properties of the local linear quantile estimator under the extremal order quantile asymptotics, and develops a practical inference method for conditional quantiles in extreme tail areas. By using a point process technique, the asymptotic distribution of the local linear quantile estimator is derived as a minimizer of certain functional of a Poisson point process that involves nuisance parameters. To circumvent difficulty of estimating those nuisance parameters, we propose a subsampling inference method for conditional extreme quantiles based on a self-normalized version of the local linear estimator. A simulation study illustrates usefulness of our subsampling inference to investigate extremal phenomena.

Suggested Citation

  • Daisuke Kurisu & Taisuke Otsu, 2021. "Nonparametric inference for extremal conditional quantiles," STICERD - Econometrics Paper Series 616, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:616
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    References listed on IDEAS

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    1. He, Fengyang & Cheng, Yebin & Tong, Tiejun, 2016. "Estimation of extreme conditional quantiles through an extrapolation of intermediate regression quantiles," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 30-37.
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    5. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    6. Bertail, Patrice & Haefke, Christian & Politis, D.N.Dimitris N. & White, Halbert, 2004. "Subsampling the distribution of diverging statistics with applications to finance," Journal of Econometrics, Elsevier, vol. 120(2), pages 295-326, June.
    7. Joseph Altonji & Hidehiko Ichimura & Taisuke Otsu, 2019. "Nonparametric intermediate order regression quantiles," STICERD - Econometrics Paper Series 608, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. Heiny, Johannes & Mikosch, Thomas, 2017. "Eigenvalues and eigenvectors of heavy-tailed sample covariance matrices with general growth rates: The iid case," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2179-2207.
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    10. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    More about this item

    Keywords

    Quantile regression; Extreme value theory; Point process; Subsampling;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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