Bayesian frequentist hybrid inference
Bayesian frequentist hybrid inference
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DOI：
10.1214/08-aos649
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发表时间：
2009-08
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通讯作者：
A. Yuan
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文献类型：
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作者：
A. Yuan
贝叶斯方法和频率方法在许多方面不同，但有一些基本的最优性性质。在实践中，有些情况下，根据某些标准，其中一种方法更受欢迎。我们考虑关于一组多参数的推理，这些参数可以分为两个不相交的子集。在一组中，频率法可能更受青睐，而在另一组中，贝叶斯方法可能更受青睐。这引发了一种联合估计过程，即在同一参数模型中，部分参数用贝叶斯估计，其余参数用最大似然估计，这样既保留了两种方法的优点，又避免了它们的缺点。这样的混合过程在实现整体推理优势方面给了我们更大的灵活性。我们研究了所提出的估计量的相合性和高阶渐近性，并举例说明了它的应用。同时，这些结果也为目标先验的构造提供了一种新的方法。
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a set of multiple parameters, which can be divided into two disjoint subsets. On one set, a frequentist method may be favored and on the other, the Bayesian. This motivates a joint estimation procedure in which some of the parameters are estimated Bayesian, and the rest by the maximum-likelihood estimator in the same parametric model, and thus keep the strengths of both the methods and avoid their weaknesses. Such a hybrid procedure gives us more flexibility in achieving overall inference advantages. We study the consistency and high-order asymptotic behavior of the proposed estimator, and illustrate its application. Also, the results imply a new method for constructing objective prior.