Modified Least Trimmed Quantile Regression to Overcome Effects of Leverage Points

Table 1

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 10%, 20%, and 30% for the first experiment.

Sample size	Contamination rate		10%		20%		30%
	Tau	Methods	RMSE	MAE	RMSE	MAE	RMSE	MAE
100	0.25	QReg	23.7652	7.9886	34.5250	15.6395	29.6037	18.6166
		LTQReg (20%)	1.0111	0.7997	1.3567	0.9870	17.5208	7.0508
		LTQReg (30%)	0.8256	0.6668	0.9691	0.7708	1.2864	0.9324
		RWLTQReg	0.5645	0.4622	0.6352	0.5171	4.5239	3.7996
		RMD-LTQReg	0.6183	0.5049	0.6562	0.5310	0.6784	0.5492
		GM6-LTQReg	0.9434	0.7543	1.0365	0.8177	1.2492	0.9029
	0.50	QReg	23.2466	7.7603	22.8781	13.7647	26.8218	17.0167
		LTQReg (20%)	0.7788	0.6114	1.1549	0.8252	8.3452	6.7991
		LTQReg (30%)	0.5973	0.4803	0.7407	0.5839	6.7834	5.5281
		RWLTQReg	0.3919	0.3157	1.3174	1.0960	4.0146	3.2788
		RMD-LTQReg	0.4389	0.3544	0.4641	0.3739	0.4857	0.3917
		GM6-LTQReg	0.6926	0.5512	0.9085	0.6744	7.6986	6.1182
	0.75	QReg	17.1983	11.0353	23.7787	19.3859	28.4886	24.1319
		LTQReg (20%)	4.0678	3.3538	14.9824	12.4491	22.1116	18.6020
		LTQReg (30%)	3.6118	2.9751	13.1301	10.9304	19.6022	16.4446
		RWLTQReg	4.1062	3.3109	10.1311	8.1356	15.6859	12.7729
		RMD-LTQReg	0.6267	0.5088	0.6854	0.5560	0.7710	0.6227
		GM6-LTQReg	2.9753	1.2881	16.1177	13.1634	24.4130	20.5151
200	0.25	QReg	24.1181	8.1252	32.1859	14.4208	31.0170	18.4829
		LTQReg (20%)	1.0604	0.8539	1.4644	1.0847	15.3258	6.3742
		LTQReg (30%)	0.8840	0.7276	1.0497	0.8465	1.4660	1.0884
		RWLTQReg	0.6256	0.5240	0.7207	0.5994	0.8308	0.6854
		RMD-LTQReg	0.6479	0.5396	0.7301	0.6030	0.8101	0.6651
		GM6-LTQReg	1.0388	0.8399	1.1369	0.9069	1.2498	0.9808
	0.50	QReg	23.5486	7.9332	23.5468	12.8543	26.4878	16.6496
		LTQReg (20%)	0.8420	0.6735	1.2309	0.8951	7.9088	5.8414
		LTQReg (30%)	0.6562	0.5365	0.8053	0.6448	1.2468	0.8983
		RWLTQReg	0.4006	0.3322	0.7993	0.6658	1.1482	0.9557
		RMD-LTQReg	0.4748	0.3919	0.5244	0.4302	0.5696	0.4662
		GM6-LTQReg	0.7638	0.6176	0.8888	0.7017	1.2270	0.8142
	0.75	QReg	17.2519	11.0336	24.1359	19.3725	28.2692	23.0904
		LTQReg (20%)	1.0653	0.8564	12.7057	10.6259	19.9887	16.5240
		LTQReg (30%)	0.8839	0.7258	10.9569	9.1502	17.4184	14.3180
		RWLTQReg	2.7474	2.2629	8.4783	6.8885	13.6166	11.0773
		RMD-LTQReg	0.6651	0.5525	0.7408	0.6122	0.8233	0.6760
		GM6-LTQReg	1.3506	1.0279	13.5634	11.3055	21.4860	17.7558