Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 108, Issue 503, Pages 1062-1074Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2013.820134
Keywords
Box Cox power transformation; Extreme value; Heavy-tailed distribution; High quantile; Quantile regression
Categories
Funding
- NSF [DMS-1007420, DMS-1149355]
- NNSFC [11171074, 71232008]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007420] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1149355] Funding Source: National Science Foundation
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The estimation of extreme conditional quantiles is an important issue in numerous disciplines. Quantile regression (QR) provides a natural way to capture the covariate effects at different tails of the response distribution. However, without any distributional assumptions, estimation from conventional QR is often unstable at the tails, especially for heavy-tailed distributions due to data sparsity. In this article, we develop a new three-stage estimation procedure that integrates QR and extreme value theory by estimating intermediate conditional quantiles using QR and extrapolating these estimates to tails based on extreme value theory. Using the power-transformed QR, the proposed method allows more flexibility than existing methods that rely on the linearity of quantiles on the original scale, while extending the applicability of parametric models to borrow information across covariates without resorting to nonparametric smoothing. In addition, we propose a test procedure to assess the commonality of extreme value index, which could be useful for obtaining more efficient estimation by sharing information across covariates. We establish the asymptotic properties of the proposed method and demonstrate its value through simulation study and the analysis of a medical cost data. Supplementary materials for this article are available online.
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