  Expectile, first introduced by Newey and Powell (1987) 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. 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 non-linearity, non-additivity 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.
