Paper Title:

Revisiting Asymptotic Theory for Principal Component Estimators of Approximate Factor Models

Published on:

1 November 2023

Primary Category:

Statistics Theory

Paper Authors:

Peiyun Jiang,

Yoshimasa Uematsu,

Takashi Yamagata

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Shows existence of pseudo-true rotation for approximate factor models

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Proves consistency of PC estimators for pseudo-true parameters

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Derives asymptotic normality of PC estimators

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Allows for weak factor models with differing strength

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Applies approach to factor augmented regressions

Principal components for approximate factor models

This paper explores what the principal component estimators actually estimate for approximate factor models. It shows that under mild assumptions, the model can be rotated to a pseudo-true version that is separately identifiable. The paper proves consistency and asymptotic normality of the estimators relative to this pseudo-true parameter.

Principal components estimation for high dimensional factor models with weak factor loadings

Probabilistic Principal Component Analysis Consistency

Capturing variation in functional data via Bayesian modeling

Differentially Private Estimation of Principal Components and Covariance

Strong consistency of rank-constrained total least squares regression

Estimating covariance matrices for high-dimensional functional data using factor models

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