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. Author manuscript; available in PMC: 2013 Sep 12.
Published in final edited form as: Ann Stat. 2011;39(6):3234–3261. doi: 10.1214/11-AOS937

Table 1.

Simulation results to evaluate the finite sample properties of Theorem 3.1. Presented are the expected value, simulated probability of being less than 5th, 25th, 50th, 75th and 95th percentile of the normal distribution, the simulated covariance matrix and the theoretical covariance matrix for RrD,r (t). 10000 simulations were performed for each scenario.

Mean 5th %tile 25th %tile 50th %tile 75th %tile 95th %tile Observed Theoretical
Covariance Matrix Covariance Matrix
nD = 50, n = 50
R0.4,0.7(0.4) 0.01 0.05 0.17 0.46 0.63 0.98 0.1 0.117 0.079 0.103 0.104 0.129 0.081 0.104
R1,1(0.4) 0.02 0.07 0.2 0.44 0.74 0.97 0.318 0.104 0.262 0.322 0.104 0.26
R0.4,0.7(0.2) 0.03 0.04 0.22 0.47 0.73 0.96 0.161 0.201 0.171 0.225
R1,1(0.2) 0.05 0.04 0.2 0.47 0.68 0.93 0.544 0.563

nD = 100, n = 100
R0.4,0.7(0.4) 0.01 0.05 0.21 0.41 0.78 0.97 0.101 0.12 0.08 0.102 0.104 0.129 0.081 0.104
R1,1(0.4) 0.02 0.05 0.24 0.48 0.76 0.96 0.318 0.104 0.26 0.322 0.104 0.26
R0.4,0.7(0.2) 0.03 0.04 0.2 0.45 0.73 0.95 0.164 0.205 0.171 0.225
R1,1(0.2) 0.05 0.04 0.23 0.47 0.73 0.95 0.55 0.563

nD = 200, n = 200
R0.4,0.7(0.4) 0.01 0.06 0.22 0.44 0.7 0.96 0.104 0.121 0.081 0.102 0.104 0.129 0.081 0.104
R1,1(0.4) 0.02 0.05 0.25 0.48 0.72 0.95 0.317 0.104 0.259 0.322 0.104 0.26
R0.4,0.7(0.2) 0.03 0.04 0.25 0.5 0.7 0.94 0.168 0.212 0.171 0.225
R1,1(0.2) 0.05 0.05 0.23 0.46 0.72 0.95 0.555 0.563