Conditional Ordering Using Nonparametric Expectiles
Yves Aragon, Sandrine Casanova, Ray Chambers and Eve Leconte
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 nonaverage individuals is of interest. The aim is to demonstrate how an individual expectile-order, based on nonparametric estimation of the expectile regression function, can also be used to define a conditional ordering of the individuals 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-Pyrénées region of France during 1999.
Conditional expectile, expectile regression, asymmetric regression, local regression, monotonization techniques, order estimation, ordering index