# Quantile and Expectile Regression

• Thomas W. Yee
Chapter
Part of the Springer Series in Statistics book series (SSS)

## Abstract

This chapter looks at several methods for quantile and expectile regression that fall within the VGLM/VGAM framework. The following main categories are described: LMS-type quantile regression methods, the classical method (based on a loss or check function) and its connection with the asymmetric Laplace distributions (ALD), and expectile regression. A parallelism assumption for the ALD and ER allows for one solution to the quantile-crossing problem. The location parameter of the ALD can be modelled using link functions, therefore responses such as counts can be potentially handled. A second solution to the quantile-crossing problem is called the ‘onion’ method, which is likened to estimating successive layers of an onion. The VGAM package is used to illustrate the models.

## Keywords

Quantile Regression Expected Shortfall Constraint Matrice Approximate Likelihood Error Loss Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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