Power Enhancement for Dimension Detection of Gaussian Signals

Abstract

In the present section, our objective is to provide Monte-Carlo simulation results to corroborate the conclusions drawn from Proposition 1 and in Section 4. In the first simulation exercise, the objective is to illustrate Proposition 1. We generated M = 10, 000 independent samples of i.i.d. observations X (b) 1 , . . . ,X (b) 10,000, for b = 0, 1 4 , 1 2 , 1. The X (b) i ’s are i.i.d. with a common (p = 8)-dimensional Gaussian distribution with mean zero and covariance matrix