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A location‐scale model for non‐crossing expectile curves
Author(s) -
Schnabel Sabine K.,
Eilers Paul H.C.
Publication year - 2013
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.27
Subject(s) - quantile , smoothing , scale (ratio) , bundle , mathematics , set (abstract data type) , least squares function approximation , econometrics , mathematical optimization , statistics , computer science , physics , materials science , estimator , composite material , programming language , quantum mechanics
In quantile smoothing, crossing of the estimated curves is a common nuisance, in particular with small data sets and dense sets of quantiles. Similar problems arise in expectile smoothing. We propose a novel method to avoid crossings. It is based on a location‐scale model for expectiles and estimates all expectile curves simultaneously in a bundle using iterative least asymmetrically weighted squares. In addition, we show how to estimate a density non‐parametrically from a set of expectiles. The model is applied to two data sets. Copyright © 2013 John Wiley & Sons Ltd
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