Flexible Expectile Regression in Reproducing Kernel Hilbert Space

TL;DR

This paper introduces KERE, a flexible nonparametric expectile regression method in reproducing kernel Hilbert space, enhancing modeling of complex relationships in risk management and finance.

Contribution

It develops a novel kernel-based expectile regression estimator with theoretical guarantees and an efficient algorithm, extending beyond traditional linear models.

Findings

KERE outperforms classical methods in simulations.

The algorithm converges linearly.

KERE effectively models complex data in real applications.

Abstract

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.