论文标题
模拟马尔可夫随机场的高维推断和FDR控制
High-dimensional Inference and FDR Control for Simulated Markov Random Fields
论文作者
论文摘要
确定与响应变量相关的重要特征是各种科学领域的基本任务。本文探讨了在高维设置中模拟的马尔可夫随机字段的统计推断。我们引入了基于马尔可夫链蒙特卡洛最大似然估计（MCMC-MLE）的方法论，并具有弹性网络正则化。在MCMC方法的轻度条件下，我们受到惩罚的MCMC-MLE方法实现了$ \ ell_ {1} $ - 一致性。我们提出了一个非相关的分数测试，并建立了其渐近态性和一步估计器的分数测试以及相关的置信区间。此外，我们通过p值和电子价值的渐近行为构建了两个错误的发现率控制程序。全面的数值模拟证实了所提出方法的理论有效性。
Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a methodology based on Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization. Under mild conditions on the MCMC method, our penalized MCMC-MLE method achieves $\ell_{1}$-consistency. We propose a decorrelated score test, establishing both its asymptotic normality and that of a one-step estimator, along with the associated confidence interval. Furthermore, we construct two false discovery rate control procedures via the asymptotic behaviors for both p-values and e-values. Comprehensive numerical simulations confirm the theoretical validity of the proposed methods.
