Projected principal component analysis in factor models

Jianqing Fan Yuan Liao Weichen Wang

Statistics Theory and Methods mathscidoc:1912.43317

Annals of statistics, 44, (1), 219, 2016.2
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are related to the projected linear space. When the dimensionality is large, the factors can be estimated accurately even when the sample size is finite. We propose a flexible semi-parametric factor model, which decomposes the factor loading matrix into the component that can be explained by subject-specific covariates and the orthogonal residual component. The covariates effects on the factor loadings are further
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  title={Projected principal component analysis in factor models},
  author={Jianqing Fan, Yuan Liao, and Weichen Wang},
  booktitle={Annals of statistics},
Jianqing Fan, Yuan Liao, and Weichen Wang. Projected principal component analysis in factor models. 2016. Vol. 44. In Annals of statistics. pp.219.
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