Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions.

Area of Science:

• Statistics
• Functional Data Analysis
• Extreme Value Theory

Background:

• Conventional quantile regression is unstable for extreme tails, especially with heavy-tailed distributions and data sparsity.
• Partial functional linear models are increasingly used in complex data analysis.

Purpose of the Study:

• To propose a novel, stable estimator for extreme conditional quantiles in partial functional linear regression models.
• To address the limitations of existing methods when dealing with heavy-tailed distributions.

Main Methods:

• Utilized functional quantile regression with functional principal component analysis for robust estimation of slope functions and coefficients.
• Developed a new extrapolation technique from extreme value theory for estimating extreme conditional quantiles.

Main Results:

• Established the asymptotic normality of the proposed estimator.
• Demonstrated the estimator's finite sample performance through simulation studies.
• Applied the method to diffusion tensor imaging data in a cognitive disorder study.

Conclusions:

• The novel estimator offers a stable and robust solution for extreme conditional quantile estimation in partial functional linear models.
• The method shows promise for analyzing complex datasets, including neuroimaging data.