Abstract
For extreme events, estimation of high conditional quantiles for heavy tailed distributions is an important problem. Quantile regression is a useful method in this field with many applications. Quantile regression uses an L1-loss function, and an optimal solution by means of linear programming. In this paper, we propose a weighted quantile regression method. Monte Carlo simulations are performed to compare the proposed method with existing methods for estimating high conditional quantiles. We also investigate two real-world examples by using the proposed weighted method. The Monte Carlo simulation and two real-world examples show the proposed method is an improvement of the existing method.
Highlights
Extreme value events are highly unusual events that can cause severe harm to people and costly damage to the environment
6 Conclusions After the studies above, we can conclude: 1. Traditional mean regression are concerned with estimating the conditional mean by using the L2-loss function
Quantile regression with a L1- loss function overcomes the limitations of traditional mean regression
Summary
Extreme value events are highly unusual events that can cause severe harm to people and costly damage to the environment. When analyzing extreme value events, where the response variable y has a heavy-tailed distribution, the mean linear regression cannot be extended to non-central locations (Hao and Naiman 2007). Quantile regression offers a more complete statistical model by specifying the changes in the high conditional quantiles and it will be used to estimate values of extreme events (Yu et al 2003; Hao and Naiman 2007). The quantile regression method will be able to estimate the high conditional quantiles The quantile regression method can estimate high CO2 emission quantile curves Where 1Tn is an n-vector of 1s, X denotes the n×p design matrix, and u, v are n × 1 vectors with elements of ui, vi respectively (Koenker 2005)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Statistical Distributions and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
