High-dimensional Inference and FDR Control for Simulated Markov Random Fields

• URL: http://arxiv.org/abs/2202.05612v3
• Date: Sat, 20 Jan 2024 03:21:05 GMT
• Title: High-dimensional Inference and FDR Control for Simulated Markov Random Fields
• Authors: Haoyu Wei, Xiaoyu Lei, Yixin Han, Huiming Zhang
• Abstract summary: This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a methodology based on Maximum Chain Monte Carlo Likelihood Estimation with Elastic-net regularization.
• Score: 1.9458156037869137
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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