Optimally Combined Estimation for Tail Quantile

• Activity Number: 505
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kehui Wang*+ and Huixia Judy Wang
• Companies: North Carolina State University and North Carolina State University
• Keywords: Efficiency ; Extreme value index ; Information aggregation ; Joint quantile regression ; Optimal weights ; Regularly varying

Abstract

Quantile regression oers a convenient tool to access the relationship between a response and covariates in a comprehensive way and it is appealing especially in applications where interests are on the tails of the response distribution. However, due to data sparsity, the nite sample estimation at tail quantiles often suers from high variability. To improve the estimation eciency at the tail, we consider modeling multiple quantiles jointly for cases where the quantile slope coecients are constant at the tail. We propose two estimators, the weighted composite estimator that minimizes the weighted combined quantile objective function across quantiles, and the weighted quantile average estimator that is the weighted average of quantile-specic slope estimators. By using extreme value theory, we establish the asymptotic distributions of the two estimators at the tail, and propose a procedure for estimating the optimal weights. We show that the optimally weighted estimators improve the eciency over equally weighted estimators, and the eciency gain depends on the heaviness of the tail distribution. The performance of the proposed estimators is assessed through a simulation study an