Conditional Ordering Using Nonparametric Expectiles

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Description/Abstract

Expectile regression, and more generally $M$-quantile regression, can be used to characterise the relationship between a response variable and explanatory variables when the behaviour of "non-average" individuals is of interest. The aim of this paper is to demonstrate how an individual's expectile-order, based on nonparametric estimation of the expectile regression function, can also be used to define a conditional ordering of the individual's value relative to the values of other members of a data set. The relationship between contextual, or "grouping", variables and this ordering can then be investigated. In particular, we propose five estimators of expectile-order, which we compare via simulation. The use of estimated expectile-order to investigate grouping effects is then illustrated using data on physician prescribing behaviour in the Midi-Pyrenees region of France during 1999.