Table 3 Empirical size of the tests at 0.05 significance level under different dimensions \((p=q)\) and within-cluster correlations \((\rho _{c})\).
From: A fast kernel independence test for cluster-correlated data
\(p=q\) | \(\rho _{c}\) | HSIC | \(\text {HSIC}_{cl}\) | \(\text {HSIC}_{new}\) |
|---|---|---|---|---|
100 | 0.3 | 0.114 | 0.001 | 0.050 |
| Â | 0.5 | 0.821 | 0.000 | 0.045 |
| Â | 0.7 | 1.000 | 0.003 | 0.048 |
200 | 0.3 | 0.107 | 0.002 | 0.039 |
| Â | 0.5 | 0.893 | 0.004 | 0.046 |
| Â | 0.7 | 1.000 | 0.001 | 0.045 |
300 | 0.3 | 0.127 | 0.003 | 0.053 |
| Â | 0.5 | 0.912 | 0.002 | 0.054 |
| Â | 0.7 | 1.000 | 0.002 | 0.047 |
400 | 0.3 | 0.126 | 0.000 | 0.043 |
| Â | 0.5 | 0.919 | 0.002 | 0.040 |
| Â | 0.7 | 1.000 | 0.003 | 0.049 |
