论文标题
经验贝叶斯的非参数回归替代方法，用于同时估计
A nonparametric regression alternative to empirical Bayes approaches to simultaneous estimation
论文作者
论文摘要
对多个未知参数的同时估计是科学和技术跨越一系列重要问题的核心。当前，此类问题的最新性能是通过非参数经验贝叶斯方法实现的。但是，这些方法仍然遇到两个主要问题。首先，他们解决了一个常见的问题，但通过遵循贝叶斯推理来做到这一点，构成了哲学上的困境，这对经验贝叶斯方法论的态度有些不安。其次，它们的计算取决于某些密度估计，这些密度估计在某些复杂的同时估计问题中变得极为不可靠。在本文中，我们在规范高斯序列问题的背景下研究了这些问题。我们通过建立同时估计和惩罚非参数回归之间的联系来提出一种完全常见的非参数经验贝叶斯方法的替代方法。我们使用灵活的正则化策略（例如形状约束）来得出准确的估计器，而无需吸引贝叶斯论点。我们证明，我们的估计器实现渐近最佳的遗憾，并表明它们与模拟中的非参数经验贝叶斯方法和对空间分析的基因表达数据的分析。
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric empirical Bayes methods. However, these approaches still suffer from two major issues. First, they solve a frequentist problem but do so by following Bayesian reasoning, posing a philosophical dilemma that has contributed to somewhat uneasy attitudes toward empirical Bayes methodology. Second, their computation relies on certain density estimates that become extremely unreliable in some complex simultaneous estimation problems. In this paper, we study these issues in the context of the canonical Gaussian sequence problem. We propose an entirely frequentist alternative to nonparametric empirical Bayes methods by establishing a connection between simultaneous estimation and penalized nonparametric regression. We use flexible regularization strategies, such as shape constraints, to derive accurate estimators without appealing to Bayesian arguments. We prove that our estimators achieve asymptotically optimal regret and show that they are competitive with or can outperform nonparametric empirical Bayes methods in simulations and an analysis of spatially resolved gene expression data.
