Conditional Ordering Using Nonparametric Expectiles
Conditional Ordering Using Nonparametric Expectiles
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.
Southampton Statistical Sciences Research Institute, University of Southampton
Aragon, Yves
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Casanova, Sandrine
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Chambers, Ray
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Leconte, Eve
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25 January 2005
Aragon, Yves
df65912e-19d7-45ec-b2a0-a7f8250e4d1b
Casanova, Sandrine
22952de5-e044-4ce3-a60f-33fe9890878d
Chambers, Ray
96331700-f45e-4483-a887-fef921888ff2
Leconte, Eve
5b764041-1be6-45c7-8fc7-82656eeb860c
Aragon, Yves, Casanova, Sandrine, Chambers, Ray and Leconte, Eve
(2005)
Conditional Ordering Using Nonparametric Expectiles
(S3RI Methodology Working Papers, M05/01)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
23pp.
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Monograph
(Working Paper)
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.
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Published date: 25 January 2005
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Local EPrints ID: 14071
URI: http://eprints.soton.ac.uk/id/eprint/14071
PURE UUID: b9a05ae0-33d7-4221-9da7-3bc8b495eb2b
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Date deposited: 26 Jan 2005
Last modified: 15 Mar 2024 05:18
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Contributors
Author:
Yves Aragon
Author:
Sandrine Casanova
Author:
Ray Chambers
Author:
Eve Leconte
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