This paper proposes two Bayesian approaches to nonparametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay (1998) that allows unconstrained estimation. The second approach uses a Bayesian regression spline model (Smith and Kohn, 1996) with a mixture distribution of constrained normals as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple regression model where two functions are constrained to be monotone.
In REF , a Bayesian approach to estimate nonparametric monotone functions using restricted splines is developed.
A Bayesian approach to nonparametric monotone function estimation
Journal of the Royal Statistical Society, Series B
Mathematics