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

Table 1

Wild bootstrap standard errors of the parameters for the Concrete Compressive Strength data.

Standard error (Se)	Classical wild bootstrap			Robust wild bootstrap
	Bootols	Bootwu	Bootliu	RBootols	RBootwu	RBootliu
Data with outliers
Intercept	29.0037	27.0670	19.4559	27.1955	19.2343	16.5458
Cement	0.00899	0.00874	0.00612	0.00857	0.00641	0.00503
Blast Furnace Slag	0.01090	0.01022	0.00740	0.01047	0.00757	0.00605
Fly Ash	0.01283	0.01296	0.00864	0.01180	0.00971	0.00694
Water	0.04584	0.04129	0.02914	0.04301	0.02986	0.02566
Superplasticizer	0.09824	0.09564	0.06640	0.10253	0.07104	0.05706
Coarse Aggregate	0.01019	0.00956	0.00687	0.00928	0.00666	0.00559
Fine Aggregate	0.01113	0.01056	0.00772	0.01062	0.00772	0.00653
Age	0.00796	0.00550	0.00556	0.00301	0.00419	0.00175
Average Se	3.24553	3.02905	2.17708	3.04387	2.15305	1.85116
Data without outliers
Intercept	26.3944	20.6483	17.5582	25.5838	20.7367	16.9330
Cement	0.00856	0.00687	0.00554	0.00810	0.00666	0.00531
Blast Furnace Slag	0.01000	0.00805	0.00679	0.00984	0.00785	0.00648
Fly Ash	0.01188	0.01014	0.00757	0.01143	0.01022	0.00736
Water	0.04068	0.03051	0.02646	0.03837	0.03080	0.02580
Superplasticizer	0.09384	0.07151	0.05940	0.09498	0.07146	0.05974
Coarse Aggregate	0.00909	0.00752	0.00602	0.00903	0.00739	0.00575
Fine Aggregate	0.01047	0.00823	0.00699	0.01025	0.00826	0.00679
Age	0.00992	0.00842	0.00690	0.01016	0.00837	0.00619
Average Se	2.95431	2.31106	1.96487	2.86400	2.32086	1.89516