Table 3.

Empirical power when h(Z) is linear at the type I error rate of 0.05 with p=5, 10, and 100 genes are used to fit the model while the true number of genes is 5. 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 the resampling procedure (indexed by P).

			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
		Correlation = 0.5
Gaussian	sup	$P_{\widehat{S}}$	67	94	83	99	68	94	83	99	67	92	82	98
		$P_{\tilde{S}}$	68	94	85	99	69	94	85	99	68	92	83	99
	ρ 2	$P_{\widehat{Q}}$	69	95	86	99	69	94	84	100	67	92	82	98
		$P_{\tilde{Q}}$	72	96	88	99	71	94	86	100	69	92	84	99
Linear		$P_{\widehat{Q}}$	74	97	88	100	71	96	86	100	66	94	81	99
		$P_{\tilde{Q}}$	75	96	88	100	72	96	87	100	66	94	81	99
		Correlation = 0.2
Gaussian	sup	$P_{\widehat{S}}$	42	72	57	89	37	66	49	83	28	57	37	73
		$P_{\tilde{S}}$	49	78	65	92	42	70	56	86	34	61	48	76
	ρ 2	$P_{\widehat{Q}}$	43	74	59	90	38	67	50	84	28	57	37	73
		$P_{\tilde{Q}}$	54	82	69	94	45	72	60	87	34	62	48	76
Linear		$P_{\widehat{Q}}$	44	77	59	89	39	69	54	86	29	58	39	73
		$P_{\tilde{Q}}$	44	78	61	90	40	70	54	86	30	58	40	74