A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family
A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family
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发表时间：
2019-10
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通讯作者：
Trambak Banerjee;Qiang Liu;Gourab Mukherjee;Wengunag Sun
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作者：
Trambak Banerjee;Qiang Liu;Gourab Mukherjee;Wengunag Sun
我们开发了一个非参数经验贝叶斯（NEB）框架，用于离散线性指数族的复合估计，其中包括现代大数据应用中经常出现的广泛的离散分布。我们建议通过求解一个可扩展的凸程序来直接估计广义罗宾斯公式中的贝叶斯收缩因子，该凸程序是基于Stein差异度量的RKHS表示精心开发的。新的NEB估计框架可以灵活地将各种结构约束合并到数据驱动规则中，并提供统一的方法来进行具有规则和比例平方误差损失的复合估计。我们发展理论来证明一类NEB估计量具有强渐近性质。通过全面的仿真研究和对实际数据示例的分析，证明了NEB估计器相对于竞争方法的优越性。
We develop a Nonparametric Empirical Bayes (NEB) framework for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We propose to directly estimate the Bayes shrinkage factor in the generalized Robbins' formula via solving a scalable convex program, which is carefully developed based on a RKHS representation of the Stein's discrepancy measure. The new NEB estimation framework is flexible for incorporating various structural constraints into the data driven rule, and provides a unified approach to compound estimation with both regular and scaled squared error losses. We develop theory to show that the class of NEB estimators enjoys strong asymptotic properties. Comprehensive simulation studies as well as analyses of real data examples are carried out to demonstrate the superiority of the NEB estimator over competing methods.