代理存在时的复合决策及其在时空数据中的应用
Compound decision in the presence of proxies with an application to spatio-temporal data
摘要：
我们研究的问题，将协变量在一个复合决策设置。期望估计$n$响应变量的均值，这些响应变量是独立的且正态分布的，并且每个响应变量都伴随有协变量的向量。我们提出了一种方法，涉及非参数经验贝叶斯技术，并可被视为一个推广的著名的Fay-Herriot（1979）的方法。我们的方法的一些最优性性质被证明。我们还将其与Fay-Herriot和其他方法进行了数值比较，使用涉及时空协变量的“半真实”数据集，其目标是在许多小区域（统计区域）中估计某些比例。
英文摘要：
We study the problem of incorporating covariates in a compound decision setup. It is desired to estimate the means of $n$ response variables, which are independent and normally distributed, and each is accompanied by a vector of covariates. We suggest a method that involves non-parametric empirical Bayes techniques and may be viewed as a generalization of the celebrated Fay-Herriot (1979) method. Some optimality properties of our method are proved. We also compare it numerically with Fay-Herriot and other methods, using a `semi-real' data set that involves spatio-temporal covariates, where the goal is to estimate certain proportions in many small areas (Statistical-Areas)
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