Table 4.

Summary of results in the second simulation study with high degree of positivity violation based on 1000 Monte Carlo replications for estimating τ; all values have been multiplied by 100.

	n = 1000			n = 5000			n = 10,000
	Bias	RMSE	Coverage	Bias	RMSE	Coverage	Bias	RMSE	Coverage
${\widehat{\tau }}_{\text{AIPW}1}\text{(CC) }$	0	39	93	3	34	92	4	42	91
${\widehat{\tau }}_{\text{AIPW}1}\text{(CM) }$	3	64	92	8	122	91	0	174	91
${\widehat{\tau }}_{\text{AIPW}1}\text{(MC) }$	−1	43	92	−10	608	94	−78	3661	94
${\widehat{\tau }}_{\text{AIPW}1}\text{(MM) }$	110	333	88	2940	15,853	81	19631	140,198	81
${\widehat{\tau }}_{\text{AIPW}2}\text{(CC) }$	0	39	93	3	34	92	4	42	91
${\widehat{\tau }}_{\text{AIPW}2}\text{(CM) }$	3	64	92	8	122	91	0	174	91
${\widehat{\tau }}_{\text{AIPW}2}\text{(MC) }$	8	43	92	−7	608	94	−76	3661	94
${\widehat{\tau }}_{\text{AIPW}2}\text{(MM) }$	110	333	88	2940	15,853	81	19,631	140,198	81
$\widehat{\tau }(\text{CC})$	0	40	93	2	47	95	−7	80	93
$\widehat{\tau }(\text{CM})$	−4	48	92	1	71	92	8	87	93
$\widehat{\tau }(\text{MC})$	0	44	94	1	55	95	−9	86	91
$\widehat{\tau }(\text{MM})$	34	71	88	33	107	89	22	124	92
$\tilde{\tau }(\text{CC})$	0	40	93	2	47	95	−7	80	93
$\tilde{\tau }(\text{CM})$	−4	48	92	1	71	92	8	87	93
$\tilde{\tau }(\text{MC})$	9	41	92	6	50	95	−5	79	93
$\tilde{\tau }(\text{MM})$	34	71	88	33	107	89	22	124	92