BRIDGING FACTOR AND SPARSE MODELS

Jianqing Fan, Ricardo P. Masini, Marcelo C. Medeiros

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 principal components 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.

Original languageEnglish (US)
Pages (from-to)1692-1717
Number of pages26
JournalAnnals of Statistics
Volume51
Issue number4
DOIs
StatePublished - Aug 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • (partial) covariance structure
  • Factor models
  • high-dimensional inference
  • machine learning
  • penalized least-squares
  • prediction
  • supervised learning

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