Deterministic Sensitivity Analysis of the Factor Score Estimation in the Approximate Factor Model

Abstract

In this paper, by employing the matrix perturbation theory we present a deterministic sensitivity analysis of the factor score estimation in the approximate factor model with respect to two different but popular methods. The derived results precisely describe the mechanics of how the measurement and estimation errors bound the forward error of the estimated factor scores in first-order sense, and can also provide useful suggestions for designing efficient estimation procedures of the approximate factor models. Numerical experiments are also given to illustrate our theoretical results.

Keywords

Matrix perturbation / GLS method / Regression method / Condition number / 65F35 / 15A60 / 62H25

Funding

Natural Science Foundation of Shandong Province(ZR2020QA034)

National Natural Science Foundation of China(11671059)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature