Gaussian Processes and Bayesian Moment Estimation
Gaussian Processes and Bayesian Moment Estimation
复制标题
高斯过程和贝叶斯矩估计
DOI：
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发表时间：
2016
影响因子：
3
通讯作者：
Anna Simoni
中科院分区：
文献类型：
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作者：
J. Florens;Anna Simoni
摘要：给定一组过度识别参数θ的矩限制（MRs），我们研究了一种半参数贝叶斯推理方法，该方法在θ上不限制除MRs外的数据分布F。作为主要贡献，我们构造了一个退化高斯过程先验，该先验在θ上有条件地限制由该先验生成的F以1的概率满足MRs。我们之前的工作，甚至在更复杂的情况下，MRs的数量大于θ的维数。我们证明了θ对应的后验在计算上是方便的。此外，我们还表明，在我们的程序，具有二次准则的广义经验似然和基于有限信息的似然程序之间存在联系。我们通过证明θ的后验分布的一致性和渐近正态性，提供了我们的程序的频率验证。通过蒙特卡罗实验说明了该方法的有限样本特性，并在航空市场需求估计中提供了一个应用。
Abstract Given a set of moment restrictions (MRs) that overidentify a parameter θ, we investigate a semiparametric Bayesian approach for inference on θ that does not restrict the data distribution F apart from the MRs. As main contribution, we construct a degenerate Gaussian process prior that, conditionally on θ, restricts the F generated by this prior to satisfy the MRs with probability one. Our prior works even in the more involved case where the number of MRs is larger than the dimension of θ. We demonstrate that the corresponding posterior for θ is computationally convenient. Moreover, we show that there exists a link between our procedure, the generalized empirical likelihood with quadratic criterion and the limited information likelihood-based procedures. We provide a frequentist validation of our procedure by showing consistency and asymptotic normality of the posterior distribution of θ. The finite sample properties of our method are illustrated through Monte Carlo experiments and we provide an application to demand estimation in the airline market.