Table 1.

Nonparametric and semiparametric estimators of τ_XY for bivariate survival data with interval sampling

	τXY	$\text{Bias}({\widehat{\tau }}_{XY}^{\mathrm{n}})$	${\text{SE}}_{\mathrm{e}}({\widehat{\tau }}_{XY}^{\mathrm{n}})$	${\text{SE}}_{\mathrm{b}}({\widehat{\tau }}_{XY}^{\mathrm{n}})$	$\text{CP}({\widehat{\tau }}_{XY}^{\mathrm{n}})$	$\text{Bias}({\widehat{\tau }}_{XY}^{\mathrm{s}})$	${\text{SE}}_{\mathrm{e}}({\widehat{\tau }}_{XY}^{\mathrm{s}})$	${\text{SE}}_{\mathrm{b}}({\widehat{\tau }}_{XY}^{\mathrm{s}})$	$\text{CP}({\widehat{\tau }}_{XY}^{\mathrm{s}})$
Clayton	0·2	1·6	4·5	4·4	95·2	1·5	14·4	14·2	96·1
	0·5	2·8	3·6	3·6	94·4	1·7	9·9	9·7	96·3
	0·8	1·8	1·6	1·7	95·5	1·2	4·2	4·0	96·6
Gumbel	0·2	0·6	4·4	4·1	94·3	2·4	14·3	13·9	94·5
	0·5	0·9	3·6	3·4	94·6	−0·3	10·2	9·8	94·9
	0·8	1·1	1·5	1·3	94·8	−0·8	4·5	4·1	95·2
Frank	0·2	0·7	4·4	4·2	95·3	−1·8	15·6	15·3	95·7
	−0·1	−0·3	4·6	4·3	95·6	1·4	17·9	17·5	96·0
	−0·2	−1·0	4·6	4·4	95·4	2·0	15·7	15·3	96·3

${\widehat{\tau }}_{XY}^{\mathrm{n}}$, nonparametric estimator; ${\widehat{\tau }}_{XY}^{\mathrm{s}}$, copula model-based semiparametric estimator; Bias, empirical bias (× 10²); SE_e, empirical standard error (× 10²); SE_b, average bootstrap standard error (× 10²); CP, coverage probability.