Flexible Expectile Regression in Reproducing Kernel Hilbert Spaces

Expectile, first introduced by Newey and Powell in 1987 Newey, W. K., and Powell, J. L. (1987), “Asymmetric Least Squares Estimation and Testing,” Econometrica, 55, 819–847.[Crossref], [Web of Science ®] , [Google Scholar] in the econometrics literature, has recently become increasingly popular in risk management and capital allocation for financial institutions due to its desirable properties such as coherence and elicitability. The current standard tool for expectile regression analysis is the multiple linear expectile regression proposed by Newey and Powell in 1987 Newey, W. K., and Powell, J. L. (1987), “Asymmetric Least Squares Estimation and Testing,” Econometrica, 55, 819–847.[Crossref], [Web of Science ®] , [Google Scholar]. The growing applications of expectile regression motivate us to develop a much more flexible nonparametric multiple expectile regression in a reproducing kernel Hilbert space. The resulting estimator is called KERE, which has multiple advantages over the classical multiple linear expectile regression by incorporating nonlinearity, nonadditivity, and complex interactions in the final estimator. The kernel learning theory of KERE is established. We develop an efficient algorithm inspired by majorization-minimization principle for solving the entire solution path of KERE. It is shown that the algorithm converges at least at a linear rate. Extensive simulations are conducted to show the very competitive finite sample performance of KERE. We further demonstrate the application of KERE by using personal computer price data. Supplementary materials for this article are available online.