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.
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Yee, T.W. (2015). Quantile and Expectile Regression. In: Vector Generalized Linear and Additive Models. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2818-7_15
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DOI: https://doi.org/10.1007/978-1-4939-2818-7_15
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