Table 1:
The empirical size and computation time for our global test Ψα and the aSPU test of Kim et al. (2014). The empirical size is in percentage based on 1000 data replications. The computation time is in seconds averaged over three sparsity levels and all replications. The significance level is α = 5%, and the sample size is n1 = n2 = 500.
| Method | p = 100 | p = 200 | Computation time | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 0.2q | 0.15q | 0.1q | 0.2q | 0.15q | 0.1q | p = 100 | p = 200 | ||
| Ψα | 4.1 | 5.1 | 5.6 | 5.0 | 3.6 | 4.9 | 0.52 | 1.99 | |
| Power-law | |||||||||
| aSPU | 5.8 | 6.7 | 6.0 | 5.8 | 5.6 | 5.7 | 4.86 | 32.6 | |
| Ψα | 4.3 | 5.4 | 5.2 | 5.9 | 4.4 | 5.1 | 0.56 | 2.00 | |
| Stochastic Block | |||||||||
| aSPU | 6.2 | 6.1 | 5.5 | 6.2 | 7.0 | 5.4 | 4.66 | 32.8 | |
| Ψα | 5.3 | 5.4 | 4.1 | 4.8 | 5.4 | 5.4 | 0.52 | 2.01 | |
| Erdös-Rényi | |||||||||
| aSPU | 5.9 | 7.5 | 5.2 | 6.1 | 5.3 | 6.4 | 4.74 | 32.3 | |
| Ψα | 6.2 | 5.1 | 4.9 | 4.8 | 3.4 | 5.5 | 0.51 | 2.06 | |
| Bernoulli mixture | |||||||||
| aSPU | 6.8 | 6.3 | 5.4 | 7.0 | 5.4 | 6.0 | 4.77 | 32.9 | |
| Ψα | 4.9 | 4.5 | 5.7 | 4.2 | 4.8 | 4.5 | 0.54 | 2.23 | |
| Transformed Wishart | |||||||||
| aSPU | 6.5 | 6.9 | 6.3 | 6.5 | 6.8 | 5.7 | 4.42 | 28.1 | |