Information criteria for latent factor models: a study on factor pervasiveness and adaptivity.
Information criteria for latent factor models: a study on factor pervasiveness and adaptivity.
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DOI：
10.1016/j.jeconom.2022.03.005
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发表时间：
2022-04
影响因子：
6.3
通讯作者：
Xiaoming Guo;Yu Chen;C. Tang
中科院分区：
文献类型：
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作者：
Xiaoming Guo;Yu Chen;C. Tang
我们广泛地研究了高维潜在因素模型在一般条件下的信息准则。在仔细分析主成分分析方法的估计误差的基础上，我们建立了潜在因素得分估计精度的理论结果，考虑了可能较弱的因素渗透性的影响；我们的分析不要求所有主导因素的因素强度相同。为了估计潜在因素的数量，我们提出了一种新的惩罚规范，其中包括两方面的考虑：i)适应因素渗透性的强度，ii)倾向于更简约的模型。我们的理论证明了该方法在一般条件下的有效性。此外，我们构造了例子来证明当因素强度太弱时，存在这样的情景，即没有任何信息标准能够一致地识别潜在因素。我们用大量的数值例子来说明所提出的自适应信息准则的性能，包括模拟和实际数据分析。
We study the information criteria extensively under general conditions for high-dimensional latent factor models. Upon carefully analyzing the estimation errors of the principal component analysis method, we establish theoretical results on the estimation accuracy of the latent factor scores, incorporating the impact from possibly weak factor pervasiveness; our analysis does not require the same factor strength of all the leading factors. To estimate the number of the latent factors, we propose a new penalty specification with a two-fold consideration: i) being adaptive to the strength of the factor pervasiveness, and ii) favoring more parsimonious models. Our theory establishes the validity of the proposed approach under general conditions. Additionally, we construct examples to demonstrate that when the factor strength is too weak, scenarios exist such that no information criterion can consistently identify the latent factors. We illustrate the performance of the proposed adaptive information criteria with extensive numerical examples, including simulations and a real data analysis.