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Title: Bayesian estimation and testing for constrained multivariate functions Authors:  Tom Shively - University of Texas at Austin (United States) [presenting]
Abstract: The aim is to estimate multivariate functions nonparametrically with shape constraints such as monotonicity, convexity and quasi-convexity imposed on the function estimates. We also develop tests for whether it is appropriate to impose specific shape constraints in some or all directions. Our method uses a regression spline representation of the multivariate function and projects the unconstrained spline function into the appropriate constrained function space. Quadratic programming is used to solve for the constrained regression spline coefficients. Simulation experiments show the small sample properties of both the estimation and testing methodology.