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- Title
Extreme quantile estimation for partial functional linear regression models with heavy‐tailed distributions.
- Authors
Zhu, Hanbing; Li, Yehua; Liu, Baisen; Yao, Weixin; Zhang, Riquan
- Abstract
In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy‐tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy‐tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.
- Subjects
QUANTILE regression; REGRESSION analysis; EXTREME value theory; DIFFUSION tensor imaging; PRINCIPAL components analysis; ASYMPTOTIC normality
- Publication
Canadian Journal of Statistics, 2022, Vol 50, Issue 1, p267
- ISSN
0319-5724
- Publication type
Article
- DOI
10.1002/cjs.11653