One-way or two-way factor model for matrix sequences?

This paper investigates the issue of determining dimensions row and column factor spaces in matrix-valued data. Exploiting eigen-gap spectrum sample second moment matrices data, we propose a family randomised tests to check whether one-way or two-way structure exists not. Our do not require any arbitrary thresholding on eigenvalues, can be applied with (virtually) no restrictions relative rate divergence cross-sections sizes as they pass infinity. Although are based randomisation which does vanish asymptotically, de-randomised, “strong” (based Law Iterated Logarithm) decision rule choose favour against presence common factors. We use proposed two ways. further cast our individual sequential procedure whose output is an estimate number built variants matrix data: one (or column) “flattened” version sequence, projection-based method. simulations show that both procedures work well large samples and, small samples, projection method delivers superior performance compared existing methods virtually all cases considered.