Monte Carlo Confidence Sets for Identified Sets
识别集的蒙特卡洛置信集AI 解读 ↓
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识别集的蒙特卡洛置信集
- 研究问题
- 在参数可能仅被部分识别的复杂模型中，如何为完整参数及其子向量的识别集构造计算可行且具有频率学覆盖保证的置信集？
- 方法与思路
- 作者用最优样本准则函数的水平集构造置信集，并从准后验中蒙特卡洛模拟临界值，结合准似然比的后验极限理论。
- 材料陈述的贡献
- 摘要称规则部分识别模型具有精确渐近覆盖，边界情形可能保守，并给出奇异子向量和跨点识别、部分识别模型的一致有效性结果。
- 阅读关注点
- 应核对规则、边界与奇异情形的划分，识别集覆盖的定义、准后验构造，以及子向量剖面化和一致有效性所需条件。
- 阅读边界
- 所给版本为 arXiv 预印本，不能认定已同行评审或接收；摘要未列全适用条件，精确渐近覆盖不等于有限样本精确覆盖。
原文摘要
In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or continuously-updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations directly from the quasi-posterior distributions of the criterions. We establish new Bernstein-von Mises (or Bayesian Wilks) type theorems for the quasi-posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR in partially-identified regular models and some non-regular models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identified sets of full parameters and of subvectors in partially-identified regular models, and have valid but potentially conservative coverage in models with reduced-form parameters on the boundary. Our MC CSs for identified sets of subvectors are shown to have exact asymptotic coverage in models with singularities. We also provide results on uniform validity of our CSs over classes of DGPs that include point and partially identified models. We demonstrate good finite-sample coverage properties of our procedures in two simulation experiments. Finally, our procedures are applied to two non-trivial empirical examples: an airline entry game and a model of trade flows.