Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T00:27:59.389Z Has data issue: false hasContentIssue false

SUBSAMPLING INFERENCE FOR NONPARAMETRIC EXTREMAL CONDITIONAL QUANTILES

Published online by Cambridge University Press:  06 November 2023

Daisuke Kurisu
Affiliation:
The University of Tokyo
Taisuke Otsu*
Affiliation:
London School of Economics
*
Address correspondence to Taisuke Otsu, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper proposes a subsampling inference method for extreme conditional quantiles based on a self-normalized version of a local estimator for conditional quantiles, such as the local linear quantile regression estimator. The proposed method circumvents difficulty of estimating nuisance parameters in the limiting distribution of the local estimator. A simulation study and empirical example illustrate usefulness of our subsampling inference to investigate extremal phenomena.

Type
ARTICLES
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

References

Bashtannyu, D.M. & Hyndman, R.J. (2001) Bandwidth selection for kernel conditional density estimation. Computational Statistics & Data Analysis 36, 279298.CrossRefGoogle Scholar
Bertail, P., Haefke, C., Politis, D.N., & White, H. (2004) Subsampling the distribution of diverging statistics with applications to finance. Journal of Econometrics 120, 295326.CrossRefGoogle Scholar
Bickel, P.J. & Freedman, D.A. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 11961217.CrossRefGoogle Scholar
Chaudhuri, P. (1991) Nonparametric estimates of regression quantiles and their local bahadur representation. Annals of Statistics 19, 760777.CrossRefGoogle Scholar
Chernozhukov, V. (1998) Nonparametric Extreme Regression Quantiles. Massachusetts Institute of Technology. Working paper.Google Scholar
Chernozhukov, V. (2005) Extremal quantile regression. Annals of Statistics 33, 806839.CrossRefGoogle Scholar
Chernozhukov, V. & Fernández-Val, I. (2011) Inference for extremal conditional quantile models, with an application to market and birthweight risks. Review of Economic Studies 78, 559589.CrossRefGoogle Scholar
Chernozhukov, V., Fernández-Val, I., & Galichon, A. (2010) Quantile and probability curves without crossing. Econometrica 78, 10931125.Google Scholar
Daouia, A., Gardes, L., & Girard, S. (2013) On kernel smoothing for extremal quantile regression. Bernoulli 19, 25572589.CrossRefGoogle Scholar
Embrechts, P., Klüppelberg, C., & Mikosch, T. (1997) Modeling Extremal Events for Insurance and Finance . Springer.CrossRefGoogle Scholar
Fan, J., Hu, T.-C., & Truong, Y.K. (1994) Robust non-parametric function estimation. Scandinavian Journal of Statistics 21, 433446.Google Scholar
He, F., Cheng, Y., & Tong, T. (2016) Estimation of extreme conditional quantiles through an extrapolation of intermediate regression quantiles. Statistics & Probability Letters 113, 3037.CrossRefGoogle Scholar
Ichimura, H., Otsu, T. and Altonji, J. (2019) Nonparametric Intermediate Order Regression Quantiles. Yale University. Working paper.Google Scholar
Koenker, R. & Bassett, G. (1978) Regression quantiles. Econometrica 46, 3350.CrossRefGoogle Scholar
Phillips, P.C.B. (2015) Halbert White Jr. memorial JFEC lecture: Pitfalls and possibilities in predictive regression. Journal of Financial Econometrics 13, 521555.CrossRefGoogle Scholar
Politis, D.N., Romano, J.P., & Wolf, M. (1999) Subsampling . Springer.CrossRefGoogle Scholar
Resnick, S.I. (1987) Extreme Values, Regular Variation, and Point Process . Springer.CrossRefGoogle Scholar
Resnick, S.I. (2007) Heavy-Tail Phenomena: Probabilistic and Statistical Modeling . Springer.Google Scholar
Takeuchi, I., Le, Q.V., Sears, T., & Smola, A.J. (2006) Nonparametric quantile regression. Journal of Machine Learning Research 7, 12311264.Google Scholar
Wang, H.J., Li, D., & He, X. (2012) Estimation of high conditional quantiles for heavy-tailed distributions. Journal of American Statistical Association 107, 14531464.CrossRefGoogle Scholar
Yu, K. & Jones, M.C. (1998) Local linear quantile regression. Journal of the American Statistical Association 93, 228237.CrossRefGoogle Scholar
Zhang, Y. (2018) Extremal quantile treatment effects. Annals of Statistics 46, 37073740.CrossRefGoogle Scholar
Supplementary material: PDF

Kurisu and Otsu supplementary material

Kurisu and Otsu supplementary material

Download Kurisu and Otsu supplementary material(PDF)
PDF 601.8 KB