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： 本文旨在对非参数工具变量模型进行准贝叶斯分析，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，并在函数值参数上放置先验。 我们称由此得到的后验为准后验，这在文献中对应于“Gibbs后验”。 我们关注在缓慢增长的有限维筛子上构造的先验。 我们推导了准后验分布的收缩率以及非参数Bernstein-von Mises型结果，并推导了由后验期望定义的准贝叶斯估计量的收敛率。 我们证明，当先验适当选择时，准后验分布（准贝叶斯估计量）达到了最小最大收缩率（收敛率）。 这些结果大大改进了之前的相关工作。 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 focus on priors constructed on slowly growing finite dimensional sieves. 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.