Report title:Dimensionality determination: a thresholding double ridge ratio criterion
Reporter:Prof. ZHU Lixing (Department of Mathematics, Hong Kong Baptist University)
Report time:October 24, 2016 PM 14:30-15:30
Location:408#room, Research and education building
Contact:WANG Xiaoguang (tel: 84708351-8013)
Abstract:Popularly used eigendecomposition-based criteria such as BIC type, ratio estimation and principal component-based criterion often underestimate model dimensionality 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 dimension 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. In this paper, 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.
Brief introduction to the reporter: Prof. ZHU Lixing, received his PhD degree at Institute of System Science, Chinese Acadamy of Sciences (1990), and had a post in Institute of Applied Mathematics (1991). He worked at Statistics and actuarial science department, University of Hong Kong for seven years (1998-2005).Then he turned to be the chair professor in Hong Kong Baptist University (2005), and held the post of department chairman (2008-2014). Prof. ZHU was supported by The National Science Fund for Distinguished Young Scholars (1997), and supported by 100 Talents Program of the Chinese Academy of Sciences (1999). He worked as Yangtse Rive chair professor (2004-2007), acquired Humboldt research award from The Humboldt foundation in Germany (2000), and Second Prize of China national natural science(2013). He was elected as an member of International Statistical Institute (2003), Institute of Mathematical Statistics (2003) and Statistical society of the United States (2007).
School of Mathematical Sciences, Dalian University of Technology
October 20, 2016