Semiparametric Bayesian inference in multiple equation models
提出一种多方程模型中的贝叶斯半参数回归方法，适用于看似不相关回归或含非参数成分的联立方程模型，通过经验贝叶斯估计平滑超参数，并应用于劳动与教育回报领域的两方程结构模型。
Abstract This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal–Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two‐equation structural model drawn from the labour and returns to schooling literatures. Copyright © 2005 John Wiley & Sons, Ltd.