标题： 非参数工具变量模型的准贝叶斯分析 显示英文标题

标题： Quasi-Bayesian analysis of nonparametric instrumental variables models

摘要： 本文旨在开发非参数工具变量模型的准贝叶斯分析，重点研究准后验分布的渐近性质。 在本文中，我们不假设数据生成过程的分布假设，而是考虑从条件矩限制中得出的准似然，并对函数值参数赋予先验分布。 我们将得到的后验称为准后验，这在文献中对应于“吉布斯后验”。 我们使用筛先验，即集中在有限维筛空间上的先验分布。 筛空间的维度应随着样本量的增加而增加。 我们推导了准后验分布的收缩率和非参数Bernstein-von Mises型结果，以及由后验期望定义的准贝叶斯估计量的收敛率。 我们证明，通过适当选择先验，准后验分布（准贝叶斯估计量）达到了最小最大最优收缩率（收敛率）。 这些结果大大改进了以前的相关工作。 显示英文摘要

摘要： This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional assumption on the data generating process, we consider a quasi-likelihood induced from the conditional moment restriction, and put priors on the function-valued parameter. We call the resulting posterior quasi-posterior, which corresponds to "Gibbs posterior" in the literature. Here we use sieve priors, which are prior distributions that concentrate on finite dimensional sieve spaces. The dimension of the sieve space should increase as the sample size. We derive rates of contraction and a non-parametric Bernstein-von Mises type result for the quasi-posterior distribution, and rates of convergence for the quasi-Bayes estimator defined by the posterior expectation. We show that, with priors suitably chosen, the quasi-posterior distribution (the quasi-Bayes estimator) attains the minimax optimal rate of contraction (convergence, respectively). These results greatly sharpen the previous related work.