Table 2.

Empirical sizes at type I error rate of 0.05 for the case when the genes are weakly correlated (℘ = 0.2). Testing was performed based on (i) sup-statistic with the original kernel (subscript $\widehat{S}$); (ii) sup-statistic with the kernel PCA including 90% of eigenvalues (subscript $\tilde{S}$); (iii) score test with ρ fixed at ρ₂ (upper bound of $\mathcal{I}$) with original kernel (subscript $\widehat{Q}$); (iv) score test at ρ₂ with kernel PCA (subscript $\tilde{Q}$). The null distributions were generated based on (a) the resampling procedure (indexed by P); (b) the χ² approximation (indexed by χ² ); and (c) the normal approximation (indexed by N).

				p = 5				p = 10				p =100
Censoring %			50%		25%		50%		25%		50%		25%
Kernel		n	100	200	100	200	100	200	100	200	100	200	100	200
Gaussian	sup	$P_{\widehat{S}}$	4.8	3.6	3.4	4.0	3.3	4.5	3.0	3.6	3.5	4.6	3.0	3.0
		$P_{\tilde{S}}$	5.4	4.5	4.9	4.6	4.2	5.4	4.2	4.1	5.2	5.3	5.4	4.4
		$N_{\widehat{S}}$	6.9	5.4	5.4	6.1	4.8	6.5	4.1	4.9	4.3	5.4	4.1	4.0
		$N_{\tilde{S}}$	10.	7.4	8.2	7.8	7.1	8.2	7.1	7.3	7.0	7.1	7.6	6.2
	ρ 2	$P_{\widehat{Q}}$	5.4	3.7	3.8	4.0	3.5	4.4	3.2	4.0	3.6	4.6	3.0	3.2
		$P_{\tilde{Q}}$	6.2	4.7	5.3	4.5	4.4	5.8	4.6	4.8	5.6	5.3	5.8	4.7
		$N_{\widehat{Q}}$	7.2	5.3	5.5	6.0	4.8	6.4	4.6	4.9	4.4	5.3	4.0	4.1
		$N_{\tilde{Q}}$	8.4	6.7	7.0	6.5	6.2	7.2	6.2	6.8	7.4	7.2	8.0	6.2
		${\chi }_{\widehat{Q}}^2$	5.2	3.6	3.6	4.0	3.4	4.8	3.3	4.0	3.6	4.8	3.2	3.3
		${\chi }_{\tilde{Q}}^2$	6.0	4.6	5.3	4.4	4.4	6.0	4.6	4.8	5.5	5.3	5.9	5.0
Linear		$P_{\widehat{Q}}$	4.1	5.6	4.2	5.1	4.3	3.4	3.2	3.6	4.0	4.3	4.0	3.4
		$P_{\tilde{Q}}$	4.4	5.5	4.1	5.4	4.4	3.7	3.7	4.1	4.4	4.5	4.5	3.4
		$N_{\widehat{Q}}$	6.0	7.1	5.8	6.7	5.8	4.9	5.1	4.8	5.4	5.4	5.0	4.4
		$N_{\tilde{Q}}$	6.2	7.3	5.9	6.6	6.2	5.2	5.3	5.4	5.6	5.4	5.4	4.6
		${\chi }_{\widehat{Q}}^2$	4.0	5.4	4.2	4.8	4.2	3.3	3.3	3.6	4.4	4.6	4.2	3.4
		${\chi }_{\tilde{Q}}^2$	4.2	5.3	4.2	5.2	4.4	3.7	3.8	4.0	4.6	4.8	4.4	3.6