Table 1.

Simulation results on estimation and inference in finite p cases

Case	n	ρ		ξ1	ξ2	ξ3	ξ4
A		0	True	0.062	0.062	0.124	0.255
	200		Estimate	0.066	0.062	0.123	0.251
			Coverage	0.980	0.960	0.940	0.900
			Rejection		0.06	0.69	1
	400		Estimate	0.064	0.063	0.124	0.254
			Coverage	0.950	0.940	0.940	0.950
			Rejection		0.05	0.92	1
		0.4	True	0.181	0.181	0.209	0.270
	200		Estimate	0.182	0.183	0.212	0.271
			Coverage	0.930	0.960	0.960	0.960
			Rejection		0.05	0.46	1
	400		Estimate	0.182	0.182	0.211	0.272
			Coverage	0.930	0.970	0.960	0.950
			Rejection		0.04	0.63	1
		0.8	True	0.265	0.265	0.272	0.289
	200		Estimate	0.269	0.270	0.278	0.295
			Coverage	0.960	0.940	0.950	0.950
			Rejection		0.05	0.30	0.85
	400		Estimate	0.268	0.267	0.275	0.292
			Coverage	0.970	0.990	0.980	0.970
			Rejection		0.03	0.34	0.97
B		0	True	0.058	0.058	0.116	0.239
	200		Estimate	0.060	0.059	0.117	0.236
			Coverage	0.970	0.980	0.910	0.930
			Rejection		0.07	0.69	1
	400		Estimate	0.060	0.059	0.117	0.236
			Coverage	0.950	0.940	0.950	0.940
			Rejection		0.03	0.89	1
		0.4	True	0.174	0.174	0.202	0.259
	200		Estimate	0.176	0.176	0.203	0.260
			Coverage	0.940	0.940	0.920	0.960
			Rejection		0.08	0.46	1
	400		Estimate	0.174	0.175	0.202	0.262
			Coverage	0.940	0.950	0.960	0.950
			Rejection		0.04	0.59	1
		0.8	True	0.258	0.258	0.264	0.281
	200		Estimate	0.262	0.261	0.271	0.287
			Coverage	0.930	0.940	0.950	0.960
			Rejection		0.10	0.30	0.86
	400		Estimate	0.261	0.260	0.268	0.284
			Coverage	0.950	0.970	0.940	0.980
			Rejection		0.04	0.26	0.95

True: true value of ξ; Estimate: average of the estimated SII; Coverage: coverage rate of the 95% bootstrap confidence intervals; Rejection: average rejection rate for the permutation test comparing ξ_j to ξ₁