论文标题
通过最小距离方法对泊松模型的最佳经验贝叶斯估计
Optimal empirical Bayes estimation for the Poisson model via minimum-distance methods
论文作者
论文摘要
Robbins估计量是Poisson模型的经验贝叶斯文献中最具标志性和广泛使用的程序。一方面，对于各种非参数先验的遗憾，这种方法最近已被证明是最小的（贝叶斯甲骨文对贝叶斯甲骨文的过多风险）而言是最佳的。另一方面，在实践中，长期以来一直认识到Robbins估计量缺乏贝叶斯估计器的所需平滑度和单调性，并且很容易被以前很少观察到的数据点而脱轨。基于最小距离距离方法，我们提出了一套经验贝叶斯估计量，包括经典的非参数最大可能性，在各种合成和真实的数据集中都超过了罗宾斯方法，并以Minimax的遗憾保持了其最优性。
The Robbins estimator is the most iconic and widely used procedure in the empirical Bayes literature for the Poisson model. On one hand, this method has been recently shown to be minimax optimal in terms of the regret (excess risk over the Bayesian oracle that knows the true prior) for various nonparametric classes of priors. On the other hand, it has been long recognized in practice that Robbins estimator lacks the desired smoothness and monotonicity of Bayes estimators and can be easily derailed by those data points that were rarely observed before. Based on the minimum-distance distance method, we propose a suite of empirical Bayes estimators, including the classical nonparametric maximum likelihood, that outperform the Robbins method in a variety of synthetic and real data sets and retain its optimality in terms of minimax regret.
