Learning Rates for Kernel-Based Expectile Regression
This work provides incremental improvements in learning rates for kernel-based expectile regression, which is important for applications in finance and other domains.
The paper tackles the problem of estimating conditional expectiles using a support vector machine approach with Gaussian RBF kernels, establishing minimax optimal learning rates (modulo a logarithmic factor) for smooth expectiles, which improves upon the best known rates for kernel-based least squares regression in this scenario.
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 improve the best known rates for kernel-based least squares regression in this 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.