Table 7:

n_k = 300, strongly heterogeneous covariate distribution

CFS	CCOD	CP	s.d.(CP)	wd	s.d.(wd)	CP	s.d.(CP)	wd	s.d.(wd)
		Homoscedasticity where σ(x) = 1
		Federated I				Pooled sample
	holds	0.891	0.043	3.26	0.37	0.901	0.018	3.31	0.16
ASR	weakly violated	0.893	0.039	3.28	0.40	1.000	0.000	8.85	0.50
	strongly violated	0.893	0.041	3.29	0.39	1.000	0.000	24.23	1.49
	holds	0.899	0.043	3.36	0.44	0.901	0.023	3.33	0.22
Local ASR	weakly violated	0.897	0.044	3.34	0.48	0.843	0.037	2.86	0.27
	strongly violated	0.895	0.049	3.34	0.47	0.754	0.056	2.35	0.30
	holds	0.923	0.064	4.55	6.23	0.903	0.025	3.35	0.24
CQR	weakly violated	0.922	0.055	4.49	5.18	0.904	0.043	3.41	0.42
	strongly violated	0.924	0.067	4.72	7.05	0.904	0.042	3.41	0.44
		Federated II (ours)				Target site only
	holds	0.893	0.038	3.28	0.34	0.898	0.048	3.35	0.47
ASR	weakly violated	0.895	0.034	3.29	0.34	0.898	0.043	3.34	0.41
	strongly violated	0.896	0.036	3.30	0.35	0.896	0.049	3.35	0.47
	holds	0.903	0.040	3.39	0.43	0.904	0.058	3.50	0.66
Local ASR	weakly violated	0.900	0.041	3.37	0.46	0.904	0.056	3.48	0.64
	strongly violated	0.900	0.043	3.37	0.44	0.905	0.058	3.50	0.63
	holds	0.927	0.051	4.38	4.96	0.918	0.058	3.68	0.66
CQR	weakly violated	0.926	0.045	4.33	4.12	0.920	0.062	3.71	0.71
	strongly violated	0.928	0.055	4.52	5.62	0.920	0.060	3.71	0.69
		Federated III				Equal weights
	holds	0.897	0.036	3.31	0.34	0.907	0.037	3.44	0.46
ASR	weakly violated	0.899	0.032	3.32	0.32	0.907	0.036	3.44	0.44
	strongly violated	0.900	0.034	3.34	0.35	0.908	0.039	3.46	0.47
	holds	0.914	0.038	3.59	1.08	0.929	0.042	4.27	3.11
Local ASR	weakly violated	0.912	0.037	3.55	0.89	0.930	0.042	4.70	7.53
	strongly violated	0.913	0.039	3.53	0.57	0.930	0.042	4.30	4.39
	holds	0.949	0.033	4.59	3.44	0.965	0.034	9.82	52.91
CQR	weakly violated	0.946	0.035	4.55	3.13	0.960	0.056	6.84	8.83
	strongly violated	0.950	0.031	4.65	4.31	0.966	0.032	6.82	7.94
		Heteroscedasticity where $\sigma (x)=-\log (x)$
		Federated I				Pooled sample
	holds	0.903	0.038	4.23	1.05	0.906	0.017	4.10	0.42
ASR	weakly violated	0.902	0.035	4.16	0.90	0.983	0.004	9.22	0.52
	strongly violated	0.904	0.034	4.21	0.95	1.000	0.000	24.37	1.53
	holds	0.918	0.053	3.92	0.89	0.925	0.032	3.89	0.49
Local ASR	weakly violated	0.919	0.053	3.97	0.92	0.870	0.044	3.19	0.45
	strongly violated	0.919	0.052	3.96	0.91	0.789	0.058	2.55	0.40
	holds	0.915	0.134	9.13	47.58	0.850	0.155	3.29	0.56
CQR	weakly violated	0.916	0.127	4.57	8.47	0.854	0.169	3.43	0.72
	strongly violated	0.915	0.126	5.86	16.05	0.839	0.183	3.48	0.91
		Federated II (ours)				Target site only
	holds	0.905	0.034	4.23	0.97	0.899	0.046	4.24	1.29
ASR	weakly violated	0.905	0.031	4.20	0.84	0.905	0.044	4.39	1.33
	strongly violated	0.906	0.030	4.22	0.87	0.902	0.042	4.28	1.27
	holds	0.920	0.049	3.96	0.91	0.901	0.091	4.12	1.67
Local ASR	weakly violated	0.923	0.050	4.04	0.94	0.913	0.085	4.31	1.70
	strongly violated	0.923	0.049	4.03	0.93	0.913	0.081	4.32	1.71
	holds	0.925	0.120	8.10	38.03	0.855	0.213	3.97	1.46
CQR	weakly violated	0.926	0.116	4.49	6.77	0.877	0.197	4.18	1.51
	strongly violated	0.929	0.107	5.53	12.80	0.877	0.192	4.18	1.49
		Federated III				Equal weights
	holds	0.910	0.031	4.38	1.00	0.918	0.031	4.69	1.25
ASR	weakly violated	0.909	0.030	4.34	0.86	0.915	0.030	4.52	0.96
	strongly violated	0.910	0.030	4.35	0.86	0.917	0.029	4.61	0.99
	holds	0.936	0.044	4.27	1.02	0.951	0.038	4.99	2.81
Local ASR	weakly violated	0.936	0.046	4.41	1.81	0.948	0.041	5.64	9.58
	strongly violated	0.938	0.047	4.42	1.66	0.950	0.040	5.40	7.17
	holds	0.958	0.097	7.31	18.71	0.975	0.066	16.39	86.25
CQR	weakly violated	0.958	0.092	5.51	7.78	0.969	0.084	13.30	53.84
	strongly violated	0.969	0.057	6.29	9.57	0.979	0.043	10.97	24.62

CFS: conformal score; CCOD: common conditional outcome distribution

CP: coverage probability; wd: width; s.d.: standard deviation (over 500 replications)