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2020 Statistical analysis of sparse approximate factor models
Benjamin Poignard, Yoshikazu Terada
Electron. J. Statist. 14(2): 3315-3365 (2020). DOI: 10.1214/20-EJS1745


We consider the problem of estimating sparse approximate factor models. In a first step, we jointly estimate the factor loading parameters and the error - or idiosyncratic - covariance matrix based on the Gaussian quasi-maximum likelihood method. Conditionally on these first step estimators, using the SCAD, MCP and Lasso regularisers, we obtain a sparse error covariance matrix based on a Gaussian QML and, as an alternative criterion, a least squares loss function. Under suitable regularity conditions, we derive error bounds for the regularised idiosyncratic factor model matrix for both Gaussian QML and least squares losses. Moreover, we establish the support recovery property, including the case when the regulariser is non-convex. These theoretical results are supported by empirical studies.


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Benjamin Poignard. Yoshikazu Terada. "Statistical analysis of sparse approximate factor models." Electron. J. Statist. 14 (2) 3315 - 3365, 2020.


Received: 1 March 2019; Published: 2020
First available in Project Euclid: 11 September 2020

zbMATH: 07246819
MathSciNet: MR4148233
Digital Object Identifier: 10.1214/20-EJS1745

Primary: 62F99 , 62H25

Keywords: Approximate factor analysis , non-convex regulariser , statistical consistency , support recovery


Vol.14 • No. 2 • 2020
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