Title: Estimating shape constrained functions using Gaussian processes
Authors: Xiaojing Wang - University of Connecticut (United States) [presenting]
Jim Berger - Duke University (United States)
Abstract: In many applications, economic theory often provides shape restrictions on functions of interest, such as the option pricing function must be monotonic and convex, utility function associated with rational preference should be monotone and so on. Whenever the economists want to model such economic relationships, they not only have to consider economic theory, but also have to take account of flexibility of functional forms. This motivates us to consider nonparametric modeling of functional relationships between economic variables under shape restrictions. Gaussian processes are a popular tool for nonparametric function estimation because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. The shape constraints can be then incorporated through the use of derivative processes, which are joint Gaussian processes with the original process, as long as the conditions of mean square differentiability hold. The possibilities and challenges of introducing shape constraints through Gaussian processes models are explored, and illustrated through simulations and real data examples. Computation is carried out through a Gibbs sampling scheme.