PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS

Annals of Statistics
Jianqing FanWeichen Wang

Abstract

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 modeled by the additive model via sieve approximations. By using the newly proposed Projected-PCA, the rates of convergence of the smooth factor loading matrices are obtained, which are much faster than those of the conventional factor analysis. The convergence is achieved even when the sample size is finite and is particularly appeal...Continue Reading

References

Nov 27, 2008·Proceedings of the National Academy of Sciences of the United States of America·Jeffrey T Leek, John D Storey
Nov 6, 2010·Journal of the American Statistical Association·Bradley Efron
Dec 19, 2013·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Jianqing FanMartina Mincheva
Jan 1, 2012·Journal of the American Statistical Association·Jianqing FanWeijie Gu
Jul 22, 2015·Journal of Econometrics·Jianqing FanXiaofeng Shi

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Citations

Oct 31, 2019·Multivariate Behavioral Research·Emilio CarrizosaAlbert Satorra
May 8, 2018·Journal of Econometrics·Jianqing FanJiawei Yao
Aug 25, 2017·Annals of Statistics·Weichen Wang, Jianqing Fan
Sep 15, 2018·Annals of Statistics·Jianqing FanWeichen Wang
Apr 21, 2018·Electronic Journal of Statistics·Eric F Lock, Gen Li
Jan 1, 2018·Electronic Journal of Statistics·Jianqing FanZiwei Zhu

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