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For D-dimensional Gaussian 1-factor, bi-factor, oblique factor models and their copula-based counterparts, proxies have previously been defined to estimate the latent variables for large D. It is shown that the previously-defined proxies are asymptotically consistent and hence robust to some interpretable assumptions of weak residual conditional dependence of observed variables given the latent variables. Proofs make use of techniques of likelihoods with mis-specified models. Some simulation results provide concrete behavior of the effect of weak residual dependence and increasing D.

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Estimation of latent variables in high-dimensional factor models with weak residual dependence

  • 章节

  • 发表日期：

    2026年

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  • Xinyao Fan,
  • Harry Joe

摘要

For D-dimensional Gaussian 1-factor, bi-factor, oblique factor models and their copula-based counterparts, proxies have previously been defined to estimate the latent variables for large D. It is shown that the previously-defined proxies are asymptotically consistent and hence robust to some interpretable assumptions of weak residual conditional dependence of observed variables given the latent variables. Proofs make use of techniques of likelihoods with mis-specified models. Some simulation results provide concrete behavior of the effect of weak residual dependence and increasing D.