Table 5:

Simulation summary statistic^a for bootstrap-based rectangular confidence bands for ${\mathrm{\Lambda }}_{11}$ and F at z = 0 and z = 1, using supremum statistics. Samples were generated under the Clayton–Oakes model (9) with ${\beta }_{10}={\beta }_{01}=\gamma =\log 2$ and dependency parameter θ = 2, with z a binary variate taking values 0 and 1 with probability 0.5.

Sample size (n)		1000			250
T1 and T2 Failure%		22.6			100
		${\mathrm{\Lambda }}_{11}$
(T1,T2) Marginal		Mean Boot.	SD Boot.	95% CB	Mean Boot.	SD Boot.	95% CB
Survival Rates	${\mathrm{\Lambda }}_{11}$	$C_{0.95}({\widehat{\mathrm{\Lambda }}}_{11})$	$C_{0.95}({\widehat{\mathrm{\Lambda }}}_{11})$	Coverage	$C_{0.95}({\widehat{\mathrm{\Lambda }}}_{11})$	$C_{0.95}({\widehat{\mathrm{\Lambda }}}_{11})$	Coverage
		z = 0
(0.85, 0.85)b	0.060	0.95	0.19	0.916	0.51	0.11	0.921
(0.70, 0.70)	0.226	3.61	0.92	0.917	1.36	0.23	0.934
(0.55, 0.55)	0.500	8.47	3.46	0.837	2.60	0.41	0.920
		z = 1
(0.85, 0.85)	0.046	0.75	0.14	0.915	0.51	0.11	0.921
(0.70, 0.70)	0.189	2.34	0.39	0.920	1.36	0.23	0.934
(0.55, 0.55)	0.453	5.75	1.28	0.923	2.60	0.41	0.920
		F
(T1, T2) Marginal		Mean Boot.	SD Boot.	95% CB	Mean Boot.	SD Boot.	95% CB
Survival Rates	F	$C_{0.95}(\widehat{F})$	$C_{0.95}(\widehat{F})$	Coverage	$C_{0.95}(\widehat{F})$	$C_{0.95}(\widehat{F})$	Coverage
		z = 0
(0.85, 0.85)	0.752	1.53	0.12	0.939	1.02	0.10	0.931
(0.70, 0.70)	0.570	2.89	0.26	0.961	1.38	0.10	0.937
(0.55, 0.55)	0.422	5.89	1.80	0.928	1.60	0.10	0.932
		z = 1
(0.85, 0.85)	0.739	1.53	0.11	0.942	1.29	0.12	0.952
(0.70, 0.70)	0.538	2.32	0.16	0.952	1.66	0.12	0.946
(0.55, 0.55)	0.379	3.34	0.31	0.947	1.83	0.12	0.942

^aMean Boot $C_{0.95}({\widehat{\mathrm{\Lambda }}}_{11})$ is the average of the 95th percentiles of $W_{{\widehat{\mathrm{\Lambda }}}_{11}}(t_1,t_2)$ over the 1000 samples, each with 200 bootstrap samples, and SD Boot $C_{0.95}({\widehat{\mathrm{\Lambda }}}_{11})$ is the standard deviation of these bootstrap percentiles; 95% CB Coverage is the fraction of bootstrap-based 95% confidence bands that include ${\mathrm{\Lambda }}_{11}\left(s_1,s_2\right)$ for all $\left(s_1,s_2\right)\epsilon \left[0,t_1\right]\times \left[0,t_2\right].$ The same quantities are presented for confidence bands for F.

^bConfidence region over $[0,-\log (0.85)]\times [0,-\log (0.85)].$