On posterior consistency in nonparametric regression problems
On posterior consistency in nonparametric regression problems
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DOI：
10.1016/j.jmva.2007.01.004
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发表时间：
2007-11-01
影响因子：
1.6
通讯作者：
Schervish, Mark J.
中科院分区：
文献类型：
--
作者：
Choi, Taeryon;Schervish, Mark J.
我们提供了充分的条件，建立后验一致性的非参数回归问题的高斯误差时，合适的先验分布用于未知的回归函数和噪声方差。当先验满足某些性质时，后验一致性的关键条件是构造与参数的适当邻域外部分离的检验。在适当的条件下，回归函数，我们表明存在的测试，其中的I型错误和II型错误的概率是指数小的区分真正的参数从补充的参数的适当的邻域。这些充分条件使我们能够建立几乎肯定的一致性的基础上，适当的度量与多维协变量值预先固定或从概率分布采样。我们考虑几个非参数回归问题的例子。(c)2007年爱思唯尔公司All rights reserved.
We provide sufficient conditions to establish posterior consistency in nonparametric regression problems with Gaussian errors when suitable prior distributions are used for the unknown regression function and the noise variance. When the prior under consideration satisfies certain properties, the crucial condition for posterior consistency is to construct tests that separate from the outside of the suitable neighborhoods of the parameter. Under appropriate conditions on the regression function, we show there exist tests, of which the type I error and the type II error probabilities are exponentially small for distinguishing the true parameter from the complements of the suitable neighborhoods of the parameter. These sufficient conditions enable us to establish almost sure consistency based on the appropriate metrics with multi-dimensional covariate values fixed in advance or sampled from a probability distribution. We consider several examples of nonparametric regression problems. (c) 2007 Elsevier Inc. All rights reserved.