On Identity Tests for High Dimensional Data Using RMT

Details On Identity Tests for High Dimensional Data Using RMT On Identity Tests for High Dimensional Data Using RMT

2012-03-15

arxiv.org/abs/1203.3278v2

Statistics

Methodology

17 pages, one figure, two tables

Scientific paper

In this work, we redefined two important statistics CLRT (Bai et.al., Ann. Stat. 37 (2009) 3822-3840) and LW test(Ledoit and Wolf, Ann. Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using classic sample covariances. Compared with existing CLRT, the proposed CLRT can accommodate data which have non-zero means and non-Gaussian dis- tributions and the new LW also can be applied to non-Gaussian data set. Simulations demonstrated that the tests had good properties in sizes and powers. What's more, we found CLRT is more sensitive to eigenvalues less than 1 while LW test has more advantages on detecting eigenvalues larger than 1.

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