Blog

In this talk, I will present our recent work on rank estimation methods based on information criterion. First, rank estimation can broadly be understood as estimating the number of factors in factor models, but in general there is no strict and unique definition of the number of factors. In the introductory part, I will explain that, in the asymptotic regime where both the sample size $n$ and the dimension $p$ diverge, Random Matrix Theory (RMT) provides a rigorous way to reformulate the number of factors as the “rank,” without assuming a factor model.

Next, I will introduce a unified selection consistency theorem for information criterion-based rank estimators. In the existing literature, the necessary and sufficient conditions for AIC, BIC, and GIC to achieve selection consistency, known as the “gap conditions,” have been studied. We also derived the gap conditions for six rank estimators based on PC-type and IC-type criterion. By integrating these results with the existing literature, we obtain a unified formulation of selection consistency for various information criterion-based rank estimators. In the talk, I will also discuss the implications of this theorem.

In addition, if time permits, I will present our ongoing work on a new information criterion-based rank estimator, the “extended GIC (eGIC).” The introduction of eGIC is motivated by recent developments in RMT for elliptical distribution families. I will explain that eGIC is effective in overcoming the limitations of existing rank estimators identified through the above theorem and numerical simulations.