Title: Order determination for large dimensional matrices
Authors: Lixing Zhu - Hong Kong Baptist University (Hong Kong) [presenting]
Abstract: Popularly used eigendecomposition-based criteria such as BIC type, ratio estimation and principal component-based criterion often underestimate model order for regressions or the number of factors for factor models. This longstanding problem is caused by the existence of one or two dominating eigenvalues compared to other nonzero eigenvalues. To alleviate this difficulty, we propose a thresholding double ridge ratio criterion such that the true order can be better identified. Unlike all existing eigendecomposition-based criteria, this criterion can define consistent estimate without requiring the uniqueness of minimum and can then handle possible multiple local minima scenarios. This generic strategy would be readily applied to other dimensionality or order determination problems. We systematically investigate, for general sufficient dimension reduction theory, the dimensionality determination with fixed and divergent dimensions; for local alternative models that converge to its limiting model with fewer projected covariates, discuss when the number of projected covariates can be consistently estimated, when cannot; and for ultra-high dimensional factor models, study the estimation consistency for the number of common factors. Numerical studies are conducted to examine the finite sample performance of the method.