Posterior Consistency of Factor Dimensionality in High-Dimensional Sparse Factor Models

IF 4.9 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Ilsang Ohn, Yongdai Kim
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引用次数: 8

Abstract

. Factor models aim to describe a dependence structure among high-dimensional random variables in terms of a low-dimensional unobserved random vector called a factor. One of the major practical issues of applying the factor model is to determine the factor dimensionality. In this paper, we propose a computationally feasible nonparametric prior distribution which achieves the posterior consistency of the factor dimensionality. We also derive the posterior contraction rate of the covariance matrix which is optimal when the factor dimensionality of the true covariance matrix is bounded. We conduct numerical studies that illustrate our theoretical results.
高维稀疏因子模型中因子维数的后验一致性
因子模型旨在用称为因子的低维未观测随机向量来描述高维随机变量之间的依赖结构。应用因子模型的主要实际问题之一是确定因子的维度。在本文中,我们提出了一种计算可行的非参数先验分布,它实现了因子维度的后验一致性。我们还导出了当真协方差矩阵的因子维数有界时最优的协方差矩阵的后验收缩率。我们进行了数值研究,以说明我们的理论结果。
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来源期刊
Bayesian Analysis
Bayesian Analysis 数学-数学跨学科应用
CiteScore
6.50
自引率
13.60%
发文量
59
审稿时长
>12 weeks
期刊介绍: Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.
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