Statistical analysis of factor models of high dimension

Statistical analysis of factor models of high dimension

Jushan Bai and Kunpeng Li

Source: Ann. Statist. Volume 40, Number 1 (2012), 436-465.

Abstract

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedasticities, which are jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.

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Supplementary material: Supplement to “Statistical analysis of factor models of high dimension”. In this supplement we provide the detailed proofs for Theorems 5.1–5.4 and 6.1. We also give a simple and direct proof that the EM solutions satisfy the first order conditions. Remarks are given on how to make use of matrix properties to write a faster computer program.

Digital Object Identifier: doi:10.1214/11-AOS966SUPP

Supplemental files available for subscribers.

Primary Subjects: 62H25

Secondary Subjects: 62F12

Keywords: High-dimensional factor models; maximum likelihood estimation; factors; factor loadings; idiosyncratic variances; principal components

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Permanent link to this document: http://projecteuclid.org/euclid.aos/1334581749
Digital Object Identifier: doi:10.1214/11-AOS966
Zentralblatt MATH identifier: 06075621
Mathematical Reviews number (MathSciNet): MR3014313

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