A Bayesian Approach to Non-Parametric Monotone Function Estimation
提出了两种贝叶斯方法用于非参数单调函数估计，一种基于分层贝叶斯框架，另一种使用带约束正态先验的贝叶斯回归样条模型，通过模拟和实例（经济需求函数）验证了方法的有效性。
Summary The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions 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. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. 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.