Estimation of High Conditional Quantiles for Heavy-Tailed Distributions

• 成果类型: Article
• 署名作者: Wang, Huixia Judy; Li, Deyuan; He, Xuming
• 署名单位: North Carolina State University; Fudan University; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.716382
• 发表日期: 2012
• 页码: 1453-1464
• 关键词: extreme-value; nonparametric-estimation; regression; RISK; precipitation; forecasts; index

摘要

Estimation 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.