Nonparametric Bayesian testing for monotonicity
本文采用非参数贝叶斯方法检验函数是否单调，构建了两类新检验，通过模拟证明其有限样本表现优于现有频率学派和贝叶斯方法，并研究了高斯模型中贝叶斯因子的渐近性质。
This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to improve upon existing frequentist and Bayesian methods. The asymptotic properties of the Bayes factor for comparing monotone versus nonmonotone regression functions in a Gaussian model are also studied. Our results significantly extend those currently available, which chiefly focus on determining the dimension of a parametric linear model.