Simple estimators of the intensity of seasonal occurrence

Brookhart, M Alan; Rothman, Kenneth J

doi:10.1186/1471-2288-8-67

BMC Medical Research Methodology

Table 1 Estimated bias and MSE for each estimator from the baseline simuala-tion for n = 150, 500, and 2500 based on 1,000 simulated datasets

From: Simple estimators of the intensity of seasonal occurrence

	n = 150
	BIAS × 10					MSE × 10
True R	$\hat{R}$ _D2	$\hat{R}$ _LS	$\hat{R}$ _WLS	$\hat{R}$ _MLE	$\hat{R}$ _E	$\hat{R}$ _D2	$\hat{R}$ _LS	$\hat{R}$ _WLS	$\hat{R}$ _MLE	$\hat{R}$ _E
1.05	1.93	3.07	3.07	3.12	3.17	0.85	1.51	1.51	1.55	1.63
1.30	0.63	1.87	1.86	2.05	2.04	0.90	1.32	1.30	1.38	1.51
1.55	0.23	1.59	1.57	1.65	1.94	1.51	1.90	1.84	1.83	2.32
1.80	0.16	1.63	1.60	1.62	2.28	2.35	2.82	2.66	2.63	3.86
2.05	0.18	1.75	1.68	1.72	2.84	3.31	3.94	3.65	3.71	6.29
2.30	0.37	2.06	1.99	1.99	3.85	4.68	5.62	5.04	5.01	10.06
2.55	0.60	2.44	2.33	2.34	5.18	6.30	7.67	6.72	6.85	17.16
2.80	0.83	2.84	2.66	2.69	7.35	8.53	10.51	8.94	9.22	46.54
3.05	1.10	3.30	3.03	3.06	10.27	11.34	14.20	11.67	12.29	193.5
	n = 500
	BIAS × 10					MSE × 10
True R	$\hat{R}$ _D2	$\hat{R}$ _LS	$\hat{R}$ _WLS	$\hat{R}$ _MLE	$\hat{R}$ _E	$\hat{R}$ _D2	$\hat{R}$ _LS	$\hat{R}$ _WLS	$\hat{R}$ _MLE	$\hat{R}$ _E
1.05	0.75	1.29	1.29	1.33	1.30	0.16	0.28	0.28	0.30	0.29
1.30	-0.07	0.49	0.49	0.52	0.53	0.26	0.28	0.28	0.28	0.29
1.55	-0.13	0.40	0.40	0.41	0.52	0.43	0.44	0.43	0.42	0.48
1.80	-0.10	0.41	0.41	0.41	0.66	0.62	0.63	0.61	0.61	0.73
2.05	-0.07	0.45	0.44	0.44	0.93	0.85	0.88	0.85	0.84	1.12
2.30	-0.05	0.49	0.47	0.47	1.29	1.14	1.19	1.12	1.12	1.66
2.55	-0.02	0.55	0.52	0.52	1.80	1.51	1.58	1.47	1.47	2.48
2.80	0.03	0.63	0.59	0.60	2.47	1.97	2.08	1.90	1.90	3.70
3.05	0.08	0.72	0.67	0.67	3.31	2.52	2.67	2.40	2.40	5.45
	n = 2500
	BIAS × 10					MSE × 10
True R	$\hat{R}$ _D2	$\hat{R}$ _LS	$\hat{R}$ _WLS	$\hat{R}$ _MLE	$\hat{R}$ _E	$\hat{R}$ _D2	$\hat{R}$ _LS	$\hat{R}$ _WLS	$\hat{R}$ _MLE	$\hat{R}$ _E
1.05	1.53	3.81	3.81	4.07	3.84	0.22	0.35	0.34	0.37	0.35
1.30	-0.64	0.89	0.87	0.86	1.02	0.58	0.55	0.55	0.55	0.57
1.55	-0.44	0.74	0.71	0.71	1.35	0.84	0.83	0.81	0.81	0.88
1.80	-0.32	0.76	0.70	0.69	2.40	1.19	1.20	1.14	1.15	1.35
2.05	-0.23	0.84	0.75	0.75	4.23	1.65	1.66	1.56	1.56	2.06
2.30	-0.13	0.97	0.85	0.82	6.98	2.22	2.24	2.07	2.07	3.18
2.55	0.00	1.15	0.97	0.92	10.77	2.93	2.96	2.69	2.70	4.94
2.80	0.16	1.37	1.15	1.11	15.76	3.79	3.83	3.43	3.44	7.73
3.05	0.28	1.58	1.28	1.24	21.98	4.80	4.86	4.27	4.29	11.99

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