Table 1.

Empirical coverage probability of 95% joint and pointwise confidence bands using FUI and 95% pointwise confidence bands using FAMM from 200 simulations. Response is Gaussian and the true fixed effects functions are S1. The pointwise confidence band is constructed as mean±2sd and the joint is mean ±q_0.975 ×sd. The baseline setting is I = 50, J = 5, L = 50, SNR_B = 0.5, SNR_ϵ =1. All other parameters are fixed at their baseline values when one sample size parameter is changed.

Method	Type	Number of subjects (l)
		50	100	200	400
FUI	Coverage (Joint)	0.93	0.96	0.94	0.95
	Coverage (Pointwise)	0.94	0.95	0.94	0.95
FAMM	Coverage	0.96	0.96	0.96	0.94
Method	Type	Mean number of visits per subject (J)
		5	10	20	40
FUI	Coverage (Joint)	0.93	0.95	0.97	0.96
	Coverage (Pointwise)	0.94	0.95	0.95	0.95
FAMM	Coverage	0.96	0.96	0.96	0.96
Method	Type	Dimension of the functional domain (L)
		50	100	200	400
FUI	Coverage (Joint)	0.93	0.94	0.94	0.94
	Coverage (Pointwise)	0.94	0.94	0.95	0.95
FAMM	Coverage	0.96	0.96	0.96	0.96