Large-Dimensional Factor Analysis Without Moment Constraints

Large-dimensional factor model has drawn much attention in the big-data era, to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model typically requires finite fourth moment of the data, which ignores the effect of heavy-tailedness and thus may result in unrobust or even inconsistent estimation of the factor space and common components. In this article, we propose to recover the factor space by performing principal component analysis to the spatial Kendall’s tau matrix instead of the sample covariance matrix. In a second step, we estimate the factor scores by the ordinary least square regression. Theoretically, we show that under the elliptical distribution framework the factor loadings and scores as well as the common components can be estimated consistently without any moment constraint. The convergence rates of the estimated factor loadings, scores, and common components are provided. The finite sample performance of the proposed procedure is assessed through thorough simulations. An analysis of a financial dataset of asset returns shows the superiority of the proposed method over the classical principle component analysis method.