本文给出形状约束条件下非参数回归模型的Bayes估计方法.利用Markov链Monte Carlo方法对模型进行拟合.具体地,用形状约束Bernstein多项式近似非参数函数,把截断正态分布作为Bernstein多项式系数的先验分布来保证函数估计满足指定的形状约束.最后通过模拟比较和实例分析来展现形状约束Bayes估计的小样本性质.
The paper proposes a Bayesian estimation method for nonparametric regression models with shape-constraints. We employ Markov chain Monte Carlo (MCMC) methods for model fitting, using a truncated normal distribution as the prior for the coefficients of Bernstein polynomials to ensure the desired shape constraints of the resulting function estimate. The small sample properties of the Bayesian shape-constrained estimators are provided via simulations and compared with existing methods. Finally a real data analysis is conducted where the nonparametric function is constrained to be monotone.