# Yasunori Fujikoshi​: High-Dimensional Properties of IC for Selection of Reduced Ranks in Sparse Multivariate Linear Model

Prof. Yasunori Fujikoshi​ (Hiroshima University​) will give a seminar in Sverdrups plass (lunch area), 8th floor, Niels Henrik Abels hus at 14:15.

Title: High-Dimensional Properties of IC for Selection of Reduced Ranks in Sparse Multivariate Linear Model

Abstract: First, we consider IC (Information Criteria) for selection of reduced ranks in multivariate regression model with $$p$$ response variables, $$q$$ explanatory variables and $$n$$ samples when the covariance matrix of response variables is  $$\Sigma = \sigma^2 I_p$$. Sufficient conditions are given for IC to be consistent in a high-dimensional situation when $$p/n \to c >0$$. We also consider IC for selecting both reduced ranks and explanatory variables. Two different approaches, due to Bunea, She and Wegkamp (AS; 2011, 2012) and Chen and Huang (JASA; 2012), are reviewed.

Next, the results are extended to IC for estimating the number of significant discriminant functions in multiple discriminant analysis. We also consider the case where $$\Sigma$$  is positive definite, based on Fujikoshi and Sakurai (JMA; 2016).

Published Aug. 11, 2016 10:35 AM - Last modified Aug. 12, 2016 11:44 AM