Estimation of High Conditional Quantiles for Heavy-Tailed Distributions
AbstractEstimation of conditional quantiles at very high or low tails is of interest in numerous applications. Quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution. However, high tails are often associated with data sparsity, so quantile regression estimation can suffer from high variability at tails especially for heavy-tailed distributions. In this article, we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors. We establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates. In a real application involving statistical downscaling of daily precipitation in the Chicago area, the proposed methods provide more stable results quantifying the chance of heavy precipitation in the area. Supplementary materials for this article are available online.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.
Volume (Year): 107 (2012)
Issue (Month): 500 (December)
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- Zhang, Qingzhao & Li, Deyuan & Wang, Hansheng, 2013. "A note on tail dependence regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 163-172.
- Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2014. "Local robust and asymptotically unbiased estimation of conditional Pareto-type tails," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(2), pages 330-355, June.
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