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Title: Robust estimation of additive boundaries with quantile regression and shape constraints Authors:  Carlos Martins-Filho - University of Colorado at Boulder (United States) [presenting]
Lan Xue - Oregon State University (United States)
Lijian Yang - Tsinghua University (China)
Yan Fang - Shanghai University of International Business and Economics (China)
Abstract: The estimation of the boundary of a set is considered when it is known to be sufficiently smooth, to satisfy certain shape constraints and to have an additive structure. The proposed method is based on spline estimation of a conditional quantile regression and is resistant to outliers and/or extreme values in the data. It extends previous work and can also be viewed as an alternative to existing estimators that have been widely used in empirical analysis. The results of a Monte Carlo study show that the new method significantly outperforms the commonly used methods when outliers or heterogeneity are present. The 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 data sets.