Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are used and the desired expectile is smooth in a Besov sense. As a special case, our learning rates improves the best known rates for kernel-based least squares regression in aforementioned scenario. Key ingredients of our statistical analysis are a general calibration inequality for the asymmetric least squares loss, a corresponding variance bound as well as an improved entropy number bound for Gaussian RBF kernels.
CITATION STYLE
Farooq, M., & Steinwart, I. (2019). Learning rates for kernel-based expectile regression. Machine Learning, 108(2), 203–227. https://doi.org/10.1007/s10994-018-5762-9
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