Shape-Constrained Density Estimation Via Optimal Transport

Optimal transportation is used to define a nonparametric density estimator as the solution of a convex optimization problem. The framework allows for density estimation subject to a variety of shape constraints, including \(\rho-\)concavity and Myerson's (1981) regularity condition. The mean in...

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Bibliographic Details
Published inarXiv.org
Main Author Cumings, Ryan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.10.2017
Subjects
Algorithms
Computational geometry
Concavity
Construction contracts
Convexity
Density
Economic models
Government agencies
Optimization
Random variables
Transportation
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Summary:Optimal transportation is used to define a nonparametric density estimator as the solution of a convex optimization problem. The framework allows for density estimation subject to a variety of shape constraints, including \(\rho-\)concavity and Myerson's (1981) regularity condition. The mean integrated squared error for the density estimator of a random variable in \(\mathbb{R}^{d}\) achieves an asymptotic rate of convergence of \(O_{p}(N^{-4/(d+4)}).\) After deriving algorithms for finding the density estimate, the framework is applied to data from the California Department of Transportation to explore whether their choice of awarding construction contracts using a first price auction is cost minimizing.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422