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通过贝叶斯非参数方法研究复合决策与经验贝叶斯AI 解读

We study compound decision theory from a nonparametric Bayesian perspective, with particular emphasis on their relationship to empirical Bayes (EB) procedures. Motivated by the sharp risk guarantees available for EB procedures based on the nonparametric maximum likelihood estimator (NPMLE), we investigate whether analogous guarantees can be established for fully Bayesian decision rules. In a class of Gaussian compound decision problems, we show that the fully Bayesian…

条件矩限制模型中的广义贝叶斯方法AI 解读

This paper develops a generalized (quasi-) Bayes framework for conditional moment restriction models, where the parameter of interest is a nonparametric structural function of endogenous variables. We establish contraction rates for a class of Gaussian process priors and provide conditions under which a Bernstein-von Mises theorem holds for the quasi-Bayes posterior. Consequently, we show that optimally weighted quasi-Bayes credible sets achieve exact asymptotic frequentist…

潜变量模型中的准贝叶斯方法AI 解读

Latent variable models are widely used to account for unobserved determinants of economic behavior. This paper introduces a quasi-Bayes approach to nonparametrically estimate a large class of latent variable models. As an application, we model U.S. individual log earnings from the Panel Study of Income Dynamics (PSID) as the sum of latent permanent and transitory components. Simulations illustrate the favorable performance of quasi-Bayes estimators relative to common…

非参数结构函数与弹性的自适应估计及一致置信带AI 解读

We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares estimators. When implemented with this choice, estimators of both the structural function $h_0$ and its derivatives (such as elasticities) converge at the fastest possible (i.e., minimax) rates in sup-norm. The second is for constructing…

条件矩限制模型中的高斯过程先验AI 解读

This paper studies quasi Bayesian estimation and uncertainty quantification for an unknown function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors. Furthermore, we provide conditions under which a Bernstein von Mises theorem holds for the quasi-posterior distribution. As a consequence, we show that optimally weighted quasi-Bayes credible sets have exact asymptotic frequentist coverage.

一般分布下的核加权模型设定检验AI 解读

Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a parametric conditional mean when the law of the regressors may not be absolutely continuous to the Lebesgue measure and is contaminated with singular components. This result is of independent interest and may be useful in other…