A class of distortion measures generated from expectile and its estimation. Issue 10 (19th May 2019)

• Record Type: Journal Article
• Authors: Wu, Sheng; Zhang, Yi
• Is Part Of: Communications in statistics. Volume 48:Issue 10(2019)
• Page Start: 2390
• Page End: 2408
• Publication Date: 2019-05-19
• Subjects: Expectile -- distortion measures -- empirical likelihood -- premium principle; C00 -- C13; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1465085
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: We construct a specific form of piecewise distortion function which can distort a random risk to its expectile. After analyzing this kind of distortion functions, we define a class of distortion functions which are generated from random variables. The consistent estimation of the expectile distortion parameter is given by the maximum empirical likelihood method. The expectile distortion not only inherits the good properties of concave distortion measures but also has its own advantages. Since that, we discuss the potential usage of this measure and imagine a new premium principle based on the non self form of this measure.