TABLE 3.

Statistics of the undersmoothed HAL fits to the individual studies, including the sample size, dimension, and number of basis functions used for the treatment model $(g)$ and the corresponding outcome model $(Q)$, the corresponding lambda penalty and the resulting $L_1$ norm

Study ID	$\mathit{n}$	$\mathit{p}$	TrueATE	Model	Undersmoothed	Num. coef.	Lambda_cv	Lambda	${\mathit{L}}_1$-norm_cv	${\mathit{L}}_1$-norm
				Q	T	167	2.6e+02	2.4e+01	5.0e−04	5.6e−03
1	418	20	−0.0109	g	T	180	7.7e+00	7.2e−01	1.6e−02	6.2e−02
				Q	T	1747	4.4e−01	3.1e−02	2.9e−02	4.5e−01
2	4863	26	0.0507	g	T	124	4.8e+00	3.9e−01	2.8e−04	1.4e−02
				Q	T	1496	2.3e−01	3.0e−02	3.5e−02	1.9e−01
3	7399	22	0.0007	g	T	6	5.2e+01	2.6e+01	7.0e−07	1.6e−03
				Q	T	503	4.9e+01	2.3e+00	5.0e−04	2.1e−02
4	1204	36	−0.0468	g	T	5	1.8e+03	3.8e+02	6.0e−07	2.2e−06
				Q	T	448	1.2e+02	4.5e+00	1.0e−04	6.9e−03
5	2396	42	−0.0136	g	T	15	8.5e+02	1.8e+02	7.0e−07	9.0e−06
				Q	T	2724	5.9e+00	3.9e−01	4.8e−03	7.6e−02
6	3265	18	0.2523	g	T	497	8.6e+00	1.1e+00	1.9e−03	2.4e−02
				Q	T	2274	5.7e−01	2.3e−02	7.6e−02	1.7e+00
7	1931	38	−0.0310	g	F	0	9.7e+01	9.7e+01	0.0e+00	0.0e+00
				Q	T	138	1.2e+01	1.4e+00	2.0e−03	2.1e−02
8	840	30	−0.0442	g	F	0	1.1e+02	1.1e+02	0.0e+00	0.0e+00
				Q	T	3700	5.4e+00	1.8e−01	2.2e−03	3.1e−02
9	27275	42	0.0089	g	T	102	1.9e+02	2.7e+01	2.2e−06	7.9e−06
				Q	T	503	1.0e+01	1.2e+00	9.0e−04	7.3e−03
10	5443	35	0.0203	g	F	0	3.5e+03	3.5e+03	0.0e+00	0.0e+00

Note: Lambda_cv and $L_1$-norm_cv from the initial HAL fit are also listed for comparison.