Modified Least Trimmed Quantile Regression to Overcome Effects of Leverage Points

Table 2

RMSE and MAE values for QReg, LTQReg (20%), LTQReg (30%), RWLTQReg, RMD-LTQReg, and GM6-LTQReg at the three quantiles 0.25, 0.50, and 0.75, in the different contamination levels 20%, 30%, and 40% for the second experiment.

Sample size	Contamination rate		10%		20%		30%
	Tau	Methods	RMSE	MAE	RMSE	MAE	RMSE	MAE
100	0.25	QReg	7.60072	2.71137	12.63955	5.40649	15.29570	7.76377
		LTQReg (20%)	0.96439	0.79551	1.12911	0.90803	2.57547	1.52490
		LTQReg (30%)	0.83776	0.69587	0.94068	0.77194	1.10528	0.89317
		RWLTQReg	0.61278	0.50790	0.70393	0.58018	0.76134	0.62801
		RMD-LTQReg	0.61412	0.50472	0.63576	0.51919	0.60821	0.49545
		GM6-LTQReg	1.00462	0.82615	1.04673	0.85208	1.07611	0.87303
	0.50	QReg	7.03403	2.49861	9.50562	4.90036	11.69555	6.27158
		LTQReg (20%)	0.75641	0.61555	1.34668	1.08131	2.43778	1.87786
		LTQReg (30%)	0.62499	0.51160	1.04447	0.85431	1.67420	1.36147
		RWLTQReg	0.39408	0.32070	0.68870	0.56272	1.01328	0.82816
		RMD-LTQReg	0.44134	0.35757	0.45001	0.36310	0.45131	0.36386
		GM6-LTQReg	0.75162	0.61254	1.10578	0.90201	1.49676	1.22331
	0.75	QReg	6.48270	2.98638	10.87028	5.68746	13.19635	6.99549
		LTQReg (20%)	1.27777	1.04650	2.76438	2.25273	3.10530	2.52145
		LTQReg (30%)	1.19103	0.98439	2.32918	1.91100	2.54114	2.09051
		RWLTQReg	0.93936	0.77860	1.59655	1.31319	1.73952	1.43453
		RMD-LTQReg	0.62520	0.51422	0.64571	0.52944	0.64247	0.52357
		GM6-LTQReg	1.33548	1.08809	2.51296	2.05925	2.42449	1.99687
200	0.25	QReg	8.09625	2.93802	12.50005	5.39671	15.54302	7.89287
		LTQReg (20%)	0.97660	0.81400	1.12126	0.91353	2.58969	1.53480
		LTQReg (30%)	0.85519	0.71915	0.93652	0.78048	1.10876	0.90673
		RWLTQReg	0.65875	0.55684	0.69650	0.58754	0.76961	0.64687
		RMD-LTQReg	0.62150	0.52297	0.61801	0.51920	0.62247	0.52132
		GM6-LTQReg	1.03788	0.85881	1.05223	0.86622	1.08009	0.88672
	0.50	QReg	7.46737	2.69586	9.44630	4.89712	11.81101	6.27112
		LTQReg (20%)	0.76073	0.62729	1.14512	0.92500	2.45982	1.97166
		LTQReg (30%)	0.62627	0.52152	0.92752	0.76556	1.81734	1.48822
		RWLTQReg	0.41374	0.34492	0.68605	0.57105	1.07019	0.89003
		RMD-LTQReg	0.41887	0.34717	0.43697	0.36076	0.41705	0.34530
		GM6-LTQReg	0.77188	0.63616	1.01386	0.82994	1.73916	1.42738
	0.75	QReg	7.45019	3.97614	10.92026	5.62669	13.21633	7.00179
		LTQReg (20%)	1.61894	1.34617	2.74805	2.27645	3.17620	2.61515
		LTQReg (30%)	1.41970	1.19561	2.36234	1.98466	2.65588	2.22840
		RWLTQReg	1.09951	0.93351	1.74217	1.48032	1.94745	1.65112
		RMD-LTQReg	0.61526	0.51805	0.63496	0.53380	0.64102	0.53548
		GM6-LTQReg	1.78427	1.46644	2.57393	2.14842	2.57785	2.16814