标题： 非参数工具变量模型的拟贝叶斯分析 显示英文标题

标题： Quasi-Bayesian analysis of nonparametric instrumental variables models

摘要： 本文旨在发展非参数工具变量模型的拟贝叶斯分析，并重点关注拟后验分布的渐近性质。本文没有假设数据生成过程的分布假设，而是考虑由条件矩限制诱导出的拟似然函数，并对函数值参数赋予先验。我们称所得的后验为拟后验，这与文献中的“Gibbs后验”相对应。本文集中讨论在增长缓慢的有限维筛子上构造的先验。我们推导了拟后验分布的收缩速度和一种非参数伯恩斯坦-冯·米塞斯型结果，以及由后验期望定义的拟贝叶斯估计量的收敛速度。我们证明，当先验被适当地选择时，拟后验分布（拟贝叶斯估计量）达到了最小最大最优的收缩速度（收敛速度，相应地）。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 nonparametric 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, resp.). These results greatly sharpen the previous related work.