Robust Estimation of Additive Boundaries With Quantile Regression and Shape Constraints

We consider the estimation of the boundary of a set when it is known to be sufficiently smooth, to satisfy certain shape constraints and to have an additive structure. Our proposed method is based on spline estimation of a conditional quantile regression and is resistant to outliers and/or extreme values in the data. This work is a desirable extension of existing works in the literature and can also be viewed as an alternative to existing estimators that have been used in empirical analysis. The results of a Monte Carlo study show that the new method outperforms the existing methods when outliers or heterogeneity are present. Our theoretical analysis indicates that our proposed boundary estimator is uniformly consistent under a set of standard assumptions. We illustrate practical use of our method by estimating two production functions using real-world datasets.

Automated summary

This paper proposes a method for estimating the boundary of a set with sufficient smoothness, certain shape constraints, and an additive structure. The method is based on spline estimation of a conditional quantile regression and is robust to outliers and/or extreme values in the data. Monte Carlo study and theoretical analysis demonstrate the superiority of the proposed method when outliers or heterogeneity are present. The practical use of the method is illustrated through estimating two production functions using real-world datasets.