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Statistics Seminar - Marcelo C. Medeiros (UIUC)

Event Type
Xiaofeng Shao
2310 Everitt Lab
Apr 13, 2023   3:30 - 5:00 pm  

Topic: Bridging Factor and Sparse Models

Abstract: Factor and sparse models are widely used to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows for efficiently exploring all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data with observable and/or latent common factors and idiosyncratic components. The model is called the factor-augmented regression model. It includes both principal component and sparse regression as specific models, significantly weakens the cross-sectional dependence, and facilitates model selection and interpretability. The method consists of several steps and a novel test for (partial) covariance structure in high dimensions to infer the remaining cross-section dependence at each step. We develop the theory for the model and demonstrate the validity of the multiplier bootstrap for testing a high-dimensional (partial) covariance structure. A simulation study and applications support the theory.

joint with Jianqing Fan and Ricardo P. Masini

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