Flexible Expectile Regression In Reproducing Kernel Hilbert Spaces

Keywords

Asymmetry least squares; Expectile regression; MM principle; Reproducing kernel Hilbert space

Abstract

Expectile, first introduced by Newey and Powell in 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 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.

Publication Date

1-2-2018

Publication Title

Technometrics

Volume

60

Issue

1

Number of Pages

26-35

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/00401706.2017.1291450

Socpus ID

85021141258 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85021141258

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