Monotonic Regression Based on Bayesian P–Splines
提出一种贝叶斯方法，利用惩罚B样条并引入单调性先验，在非参数回归中强制协变量与响应变量间的单调关系。以橙汁品牌需求为例，证明对自身和交叉价格效应施加单调约束能显著提升销售响应函数的预测准确性。
In many practical situations, it is desirable to restrict the flexibility of nonparametric estimation to accommodate a presumed monotonic relationship between a covariate and the response variable. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for brands of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response functions considerably.