Robust Wild Bootstrap for Stabilizing the Variance of Parameter Estimates in Heteroscedastic Regression Models in the Presence of Outliers

Table 2

Biasness measures of the non-robust and robust wild bootstrap.

% outliers	Coeff.	Bootols	Bootwu	Bootliu	RBootwu	RBootliu
Sample Size n = 20
0%	𝛽0	0.0115	−0.0246	−0.0070	−0.0701	−0.0799
	𝛽1	−0.5604	−0.5005	−0.4813	−0.3338	−0.2796
	𝛽2	0.3753	0.3526	0.2968	0.3576	0.3348
	Mean	0.3157	0.2926	0.2617	0.2538	0.2314
5%	𝛽0	−0.9419	−1.1981	−1.3702	0.0357	0.0821
	𝛽1	2.9588	2.8570	3.1427	−0.3130	−0.3450
	𝛽2	0.8742	1.3083	1.4716	0.4164	0.4077
	Mean	1.5916	1.7878	1.9948	0.2550	0.2783
10%	𝛽0	−5.6740	−5.3968	−5.5439	−0.2166	−0.215
	𝛽1	6.7826	6.9083	6.9500	0.2450	0.2714
	𝛽2	7.4401	6.8714	7.0577	0.4190	0.4073
	Mean	6.6322	6.3921	6.5172	0.2935	0.2979
Sample Size n = 60
0%	𝛽0	0.0197	0.0612	0.0458	−0.0123	−0.0056
	𝛽1	0.0159	−0.0189	0.0218	0.0400	0.0345
	𝛽2	0.0080	−0.0209	−0.0247	0.0462	0.0174
	Mean	0.0145	0.0337	0.0308	0.0328	0.0192
5%	𝛽0	−0.1451	−0.1466	−0.0648	−0.0190	−0.0045
	𝛽1	0.4342	0.4011	0.2954	0.0921	0.0921
	𝛽2	0.1110	0.1452	0.0526	0.0358	0.0073
	Mean	0.2301	0.2310	0.1376	0.0490	0.0346
10%	𝛽0	−0.7390	−0.7896	−0.7478	0.0164	−0.0033
	𝛽1	0.9916	0.9875	0.96302	0.0793	0.0794
	𝛽2	0.8974	1.0292	1.0004	0.0181	0.0005
	Mean	0.8760	0.9354	0.9037	0.0379	0.0277
Sample Size n = 100
0%	𝛽0	0.0226	0.0216	0.0240	−0.0505	−0.0554
	𝛽1	−0.1086	−0.1037	−0.1099	−0.0514	−0.0457
	𝛽2	−0.0448	−0.0422	−0.0433	0.0371	0.0387
	Mean	0.0587	0.0558	0.0591	0.0463	0.0466
5%	𝛽0	0.1218	0.1396	0.1095	0.0205	0.0048
	𝛽1	−0.1854	−0.3399	−0.2944	−0.1880	−0.1699
	𝛽2	−0.1944	−0.1522	−0.1174	−0.0163	−0.0038
	Mean	0.1672	0.2106	0.1738	0.0749	0.0595
10%	𝛽0	0.7546	0.6492	0.8318	−0.2921	−0.2748
	𝛽1	−1.1835	−1.0402	−1.1809	0.3250	0.3294
	𝛽2	−0.8359	−0.7686	−1.0436	0.2800	0.2558
	Mean	0.9247	0.8193	1.0187	0.2990	0.2867