Table 4.3.

Summary statistics and empirical coverage probability of 95% nominal percentile confidence intervals for ${\psi }_{11}^0$ and ${\psi }_{12}^0$ using the oracle estimator, the proposed penalized Q-learning based estimator, the hard max estimator and the soft-threshold estimator. The notations are the same as in Table 2.

	ψ11				ψ12
	bias ×1000	MSE×1000	std×100	CP	bias×1000	MSE×1000	std×100	CP
Setting 1
Oracle	−1	1.9	4.5	95.3	0	2.0	4.5	94.7
PQ	−1	1.9	4.5	95.3	0	2.0	4.5	94.7
HM	0	2.4	–	93.7*	−1	2.1	–	94.5
ST	1	2.3	–	94.8	−1	2.1	–	94.6
Setting 2
Oracle	0	2.5	5.8	97.3*	−1	2.1	4.6	95.0
PQ	−1	1.9	4.5	95.3	0	2.0	4.5	94.8
HM	0	2.5	–	94.8	−1	2.1	–	94.4
ST	1	2.3	–	94.8	0	2.1	–	94.4
Setting 3
Oracle	−1	2.9	5.5	95.0	0	2.0	4.5	94.8
PQ	−10	3.1	5.5	94.0	−1	2.0	4.5	94.6
HM	−31	4.2	–	93.8*	−1	2.1	–	94.0
ST	−11	4.0	–	95.0	0	2.1	–	94.0
Setting 4
Oracle	−26	4.0	6.2	94.9	−1	2.1	4.5	95.0
PQ	−6	3.1	5.5	94.6	0	2.0	4.5	94.6
HM	−26	4.0	–	94.5	−1	2.1	–	94.0
ST	−7	3.4	–	95.1	0	2.1	–	93.9
Setting 5
Oracle	−1	3.5	6.1	95.8	−1	2.5	4.9	94.3
PQ	−5	3.6	6.1	95.2	0	2.5	4.9	94.3
HM	−16	4.0	–	94.6	6	2.6	–	94.0
ST	−3	4.0	–	95.2	−3	2.6	–	94.2
Setting 6
Oracle	2	3.9	6.2	95.0	0	2.4	4.8	94.2
PQ	2	4.0	6.2	94.6	0	2.4	4.8	94.2
HM	2	3.9	–	93.7*	0	2.4	–	94.1
ST	1	4.6	–	91.4*	2	2.5	–	94.1