Robust estimation of functional factor models with functional pairwise spatial signs

Factor model analysis has emerged as a powerful tool to capture the latent dynamic structure of functional data from a dimension-reduction viewpoint. Conventional methods for estimating the factor model are sensitive to heavy tails and outliers. To address this issue and achieve robustness, we provide an eigenvalue-ratio based method to estimate the number of factors by replacing the covariance operator with the functional pairwise spatial sign operator. Moreover, we propose a two-step robust approach to recover the factor space. The convergence rates of the robust estimators for factor loadings, factor scores, and common components are derived under some mild conditions. Numerical studies and a real data analysis confirm the proposed procedures remain reliable even when the factors and idiosyncratic errors have heavy-tailed distributions.