Generalized quantile and expectile properties for shape constrained nonparametric estimation

Sheng Dai; Timo Kuosmanen; Xun Zhou

doi:10.1016/j.ejor.2023.04.004

Generalized quantile and expectile properties for shape constrained nonparametric estimation

Sheng Dai, Timo Kuosmanen, Xun Zhou^*

^*Corresponding author for this work

Environment and Geography

Research output: Contribution to journal › Article › peer-review

Abstract

Convex quantile regression (CQR) is a fully nonparametric approach to estimating quantile functions, which has proved useful in many applications of productivity and efficiency analysis. Importantly, CQR satisfies the quantile property, which states that the observed data is split into proportions by the CQR frontier for any weight in the unit interval. Convex expectile regression (CER) is a closely related nonparametric approach, which has the following expectile property: the relative share of negative deviations is equal to the weight of negative deviations. The first contribution of this paper is to extend these quantile and expectile properties to the general set of shape constrained nonparametric functions. The second contribution is to relax the global concavity assumptions of the CQR and CER estimators, developing the isotonic nonparametric quantile and expectile estimators. Our third contribution is to compare the finite sample performance of the CQR and CER approaches in the controlled environment of Monte Carlo simulations.

Original language	English
Pages (from-to)	914-927
Number of pages	14
Journal	European Journal of Operational Research
Volume	310
Issue number	2
DOIs	https://doi.org/10.1016/j.ejor.2023.04.004
Publication status	Published - 16 Oct 2023

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Cite this

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title = "Generalized quantile and expectile properties for shape constrained nonparametric estimation",

abstract = "Convex quantile regression (CQR) is a fully nonparametric approach to estimating quantile functions, which has proved useful in many applications of productivity and efficiency analysis. Importantly, CQR satisfies the quantile property, which states that the observed data is split into proportions by the CQR frontier for any weight in the unit interval. Convex expectile regression (CER) is a closely related nonparametric approach, which has the following expectile property: the relative share of negative deviations is equal to the weight of negative deviations. The first contribution of this paper is to extend these quantile and expectile properties to the general set of shape constrained nonparametric functions. The second contribution is to relax the global concavity assumptions of the CQR and CER estimators, developing the isotonic nonparametric quantile and expectile estimators. Our third contribution is to compare the finite sample performance of the CQR and CER approaches in the controlled environment of Monte Carlo simulations.",

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AU - Dai, Sheng

AU - Kuosmanen, Timo

AU - Zhou, Xun

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AB - Convex quantile regression (CQR) is a fully nonparametric approach to estimating quantile functions, which has proved useful in many applications of productivity and efficiency analysis. Importantly, CQR satisfies the quantile property, which states that the observed data is split into proportions by the CQR frontier for any weight in the unit interval. Convex expectile regression (CER) is a closely related nonparametric approach, which has the following expectile property: the relative share of negative deviations is equal to the weight of negative deviations. The first contribution of this paper is to extend these quantile and expectile properties to the general set of shape constrained nonparametric functions. The second contribution is to relax the global concavity assumptions of the CQR and CER estimators, developing the isotonic nonparametric quantile and expectile estimators. Our third contribution is to compare the finite sample performance of the CQR and CER approaches in the controlled environment of Monte Carlo simulations.

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