A1337
Title: Robust determination of the number of factors via divergence information criteria
Authors: Subhrajyoty Roy - Washington University in St. Louis (United States) [presenting]
Abhik Ghosh - Indian Statistical Institute (India)
Ayanendranath Basu - Indian Statistical Institute (India)
Abstract: Estimating the true rank of a noisy data matrix is a fundamental problem in multivariate statistics and econometrics, including the determination of the number of latent factors in panel data. Existing rank estimation criteria are categorized into two broad types: information-based penalization methods and cross-validation techniques. Existing information criteria are often inaccurate in the presence of outliers, even when combined with robust factorization methods. On the other hand, cross-validation approaches quickly become computationally intractable when combined with robust estimators. A new criterion is proposed, the divergence information criterion for matrix rank (DICMR), that achieves both robustness and computational simplicity. Derived from the density power divergence framework, DICMR inherits strong robustness properties while avoiding the heavy computational burdens of resampling methods. Asymptotic bounds on its overestimation and underestimation probabilities are derived and the first-order B-robustness of the criteria is demonstrated. Extensive simulations show that DICMR delivers accuracy comparable to robustified cross-validation methods but with far lower computational costs. The practical utility of DICMR is demonstrated in real-world applications, e.g., extracting latent factors from cross-country panel data, and modelling recommender systems.
