BMC Medical Research Methodology

Table 2 Outlier identification results on simulated data with p = 50

From: Outlier detection in spatial error models using modified thresholding-based iterative procedure for outlier detection approach

	Outlier = 50			Outlier = 20			Outliers = 10
	M	S	JD	M	S	JD	M	S	JD
No leverage
Spatial-hard-IPOD	0.0018	0.0564	91	0.0105	0.0518	85	0.0470	0.0420	70
Spatial-soft-IPOD	0.0024	0.0502	89	0.0190	0.0189	67	0.0600	0.0130	51
Hard-IPOD	0.2840	0.0097	47	0.2085	0.0034	51	0.2560	0.0060	57
Soft-IPOD	0.5760	0.0060	38	0.3670	0.0025	56	0.4260	0.0009	53
MM	0.3280	0.0976	35	0.2385	0.1201	55	0.2350	0.1421	57
LTS	0.3264	0.0312	28	0.2205	0.0462	44	0.2410	0.0493	49
GY	0.1632	0.1456	0	0.1050	0.1866	0	0.1390	0.2025	0
Leverage = 15
Spatial-hard-IPOD	0.0018	0.0542	92	0.0135	0.0452	82	0.0380	0.0412	74
Spatial-soft-IPOD	0.0015	0.0534	92	0.0135	0.0221	76	0.0530	0.0129	53
Hard-IPOD	0.2572	0.0191	58	0.2085	0.0014	61	0.2020	0.0030	62
Soft-IPOD	0.5077	0.0097	49	0.3600	0.0026	58	0.3470	0.0006	57
MM	0.3877	0.0625	45	0.1820	0.1329	66	0.2030	0.1419	66
LTS	0.3108	0.0305	52	0.2295	0.0416	58	0.2050	0.0493	62
GY	0.1486	0.1431	0	0.1015	0.1853	0	0.0850	0.1992	0
Leverage = 20
Spatial-hard-IPOD	0.0040	0.0513	85	0.0073	0.0438	90	0.0300	0.0440	79
Spatial-soft-IPOD	0.0025	0.0518	90	0.0094	0.0281	81	0.0370	0.0133	65
Hard-IPOD	0.2085	0.0026	60	0.2635	0.0067	52	0.1830	0.0028	69
Soft-IPOD	0.6555	0.0071	33	0.4396	0.0040	50	0.3420	0.0011	63
MM	0.2740	0.0860	55	0.2396	0.1254	58	0.1750	0.1426	72
LTS	0.2490	0.0261	48	0.3021	0.0452	50	0.1860	0.0500	64
GY	0.1050	0.1386	0	0.1469	0.1878	0	0.0840	0.1997	0

Seven methods are compared: Our proposed hard-IPOD, our proposed soft-IPOD, hard-IPOD, soft-IPOD, MM-estimator, LTS and Gervini–Yohai’s fully efficient one-step procedure

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