报告题目：Dimensionality determination: a thresholding double ridge ratiocriterion.
Popularly used eigendecomposition-basedcriteria such as BIC type, ratio estimation and principal component-basedcriterion often underdetermine model dimensionality for regressions or thenumber of factors for factor models. This longstanding problem is caused by theexistence of one or two dominating eigenvalues compared to other nonzeroeigenvalues. To alleviate this diculty, we propose a thresholding double ridgeratio criterion such that the true dimension can be better identied and is lessunderdetermined. Unlike all existing eigendecomposition-based criteria, thiscriterion can define consistent estimate without requiring the existence ofunique minimum or maximum and can then handle possible multiple local minima ormaxima scenarios. This generic strategy would be readily applied to otherdimensionality or order determination problems. In this paper, we investigate,for general sucient dimension reduction theory, the dimensionality
determination with fixed and divergentdimensions; for local alternative models that converge to its limiting modelwith fewer projected covariates, discuss when the number of projectedcovariates can be consistently estimated, when cannot; and for ultra-highdimensional factor models, study the estimation consistency for the number ofcommon factors. Numerical studies are conducted to examine the nite sampleperformance of the method.