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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Shaoxin Wang,
  • Bei Guo,
  • Hu Yang

摘要

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.