Table 2. Diagnostic measures for 1000 simulations in each null and predictive case.

Columns 4 and 5 show the bias and the $\sqrt{MSE}$ for the point estimate of the PITE. The sixth column shows the median width of the confidence intervals for the PITE, and the last columns the proportion of subjects in the identified subgroup when considering the using the limits of the confidence intervals and the point estimates. Since methods reduced and reduced-Scheffe have the same point estimate, bias and MSE are equal.

Case	n	Method	Bias	$\sqrt{MSE}$	Width	Proportion of subjects in subgroup
						% in ${\widehat{B}}_l$	% in $\widehat{B}$	% in ${\widehat{B}}_u$	% in B
Null	40	ATE	0.01	0.38	1.48	1.6	53.8	96.0	0.0
	40	full	-0.01	1.65	6.35	2.0	48.5	97.5	0.0
	40	Lasso	-0.00	0.35	5.24	0.6	45.0	93.6	0.0
	40	reduced	0.01	0.87	1.56	15.9	45.5	77.8	0.0
	40	reduced-Scheffe	0.01	0.87	5.80	0.0	45.5	94.1	0.0
	40	rLasso-1	0.00	0.86	3.37	1.4	46.9	94.0	0.0
	40	rLasso-2	-0.01	0.78	2.49	1.6	45.3	93.5	0.0
	100	ATE	-0.00	0.21	0.84	2.1	49.3	97.5	0.0
	100	full	0.02	0.76	2.90	2.2	50.7	97.8	0.0
	100	Lasso	0.01	0.22	3.00	0.9	48.0	93.4	0.0
	100	reduced	0.02	0.56	1.02	17.1	47.2	79.9	0.0
	100	reduced-Scheffe	0.02	0.56	3.24	0.0	47.2	94.7	0.0
	100	rLasso-1	0.01	0.54	2.20	1.9	48.1	94.9	0.0
	100	rLasso-2	0.02	0.46	1.61	1.6	51.2	95.6	0.0
	220	ATE	0.01	0.13	0.54	1.3	52.2	98.3	0.0
	220	full	0.00	0.47	1.79	3.1	49.9	97.7	0.0
	220	Lasso	0.00	0.16	2.15	1.2	47.2	92.9	0.0
	220	reduced	-0.01	0.38	0.73	14.2	47.2	78.0	0.0
	220	reduced-Scheffe	-0.01	0.38	2.21	0.0	47.2	93.8	0.0
	220	rLasso-1	-0.01	0.37	1.48	2.7	49.5	94.7	0.0
	220	rLasso-2	0.00	0.34	1.11	2.1	47.6	93.8	0.0
	350	ATE	-0.01	0.11	0.43	1.7	46.7	97.1	0.0
	350	full	0.01	0.39	1.40	2.8	50.7	97.3	0.0
	350	Lasso	0.00	0.13	1.60	1.3	46.3	93.9	0.0
	350	reduced	0.00	0.31	0.56	16.0	46.4	79.5	0.0
	350	reduced-Scheffe	0.00	0.31	1.65	0.0	46.4	95.7	0.0
	350	rLasso-1	0.01	0.30	1.09	2.4	48.8	94.3	0.0
	350	rLasso-2	0.00	0.28	0.86	2.3	48.2	93.8	0.0
Predictive	40	ATE	0.01	0.75	1.57	10.9	75.2	98.8	64.7
	40	full	-0.03	1.67	6.37	4.8	55.3	97.7	64.7
	40	Lasso	-0.19	0.62	6.15	2.2	54.1	96.3	64.7
	40	reduced	-0.10	0.97	1.85	24.7	54.7	81.7	64.7
	40	reduced-Scheffe	-0.10	0.97	6.72	0.0	54.7	97.6	64.7
	40	rLasso-1	-0.10	0.97	4.02	3.4	54.8	96.2	64.7
	40	rLasso-2	-0.14	0.90	3.02	3.9	53.8	94.0	64.7
	100	ATE	0.00	0.68	0.88	18.9	86.2	100.0	62.3
	100	full	0.02	0.76	2.90	13.3	61.1	95.6	62.3
	100	Lasso	-0.14	0.47	3.00	11.4	59.6	93.9	62.3
	100	reduced	-0.03	0.61	1.31	33.1	59.0	83.4	62.3
	100	reduced-Scheffe	-0.03	0.61	4.10	0.1	59.0	99.8	62.3
	100	rLasso-1	-0.04	0.61	2.52	10.6	60.0	94.0	62.3
	100	rLasso-2	-0.08	0.59	1.94	13.5	57.7	91.1	62.3
	220	ATE	0.01	0.65	0.57	44.2	96.3	100.0	61.5
	220	full	-0.00	0.47	1.79	22.1	61.0	91.4	61.5
	220	Lasso	-0.14	0.34	1.97	16.5	58.6	89.9	61.5
	220	reduced	-0.02	0.41	0.99	39.2	60.7	81.7	61.5
	220	reduced-Scheffe	-0.02	0.41	2.96	2.3	60.7	99.6	61.5
	220	rLasso-1	-0.04	0.42	1.70	19.3	59.0	89.5	61.5
	220	rLasso-2	-0.07	0.43	1.36	24.6	60.0	85.6	61.5
	350	ATE	0.01	0.63	0.45	57.5	97.8	100.0	63.5
	350	full	0.01	0.39	1.40	27.5	63.4	90.9	63.5
	350	Lasso	-0.13	0.29	1.40	24.1	58.1	88.8	63.5
	350	reduced	-0.02	0.33	0.80	41.0	61.8	79.9	63.5
	350	reduced-Scheffe	-0.02	0.33	2.38	7.2	61.8	98.7	63.5
	350	rLasso-1	-0.02	0.33	1.28	27.6	60.8	88.0	63.5
	350	rLasso-2	-0.05	0.35	1.10	29.5	60.1	84.0	63.5