Title: Information criteria for latent factor models: A study with general factor pervasiveness and adaptivity
Authors: Xiao Guo - University of Science and Technology of China (China) [presenting]
Cheng Yong Tang - Temple University (United States)
Abstract: The purpose is to study the information criteria for latent factor models, allowing large number of variables diverging with the sample size. Without requiring the factor pervasiveness condition as in existing studies, the proposal accommodates generic schemes that broadly and flexibly characterize the contributions from the latent common factors. We dedicatedly analyze the properties of the information criteria, and provide new insights on the fundamental importance from adequately incorporating the impact due to different strength of the factor pervasiveness. Based on the analysis, we then propose a class of new information criteria, adaptive to the strength of the factor pervasiveness, for identifying the number of the latent common factors. The theory establishes the consistency of the proposed adaptive information criteria in correctly determining the number of the latent factors. The analysis reveals that the adaptivity to the factor pervasiveness is indeed a key for the information criteria to be consistent in broad settings. As another new discovery, we show that when the strength of the factor pervasiveness is weak below certain level, then correctly determining the number of the latent factors is not feasible with information criteria. We demonstrate the performance of the new adaptive information criteria with extensive numerical examples including simulations and real data analysis.