Research Article
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% | | | |
−0.0070
|
−0.0701
|
−0.0799
| |
−0.5604
|
−0.5005
|
−0.4813
|
−0.3338
|
−0.2796
| |
0.3753
|
0.3526
|
0.2968
|
0.3576
|
0.3348
| Mean |
0.3157
|
0.2926
|
0.2617
|
0.2538
|
0.2314
| 5% | |
−0.9419
| | |
0.0357
|
0.0821
| |
2.9588
|
2.8570
|
3.1427
|
−0.3130
|
−0.3450
| |
0.8742
|
1.3083
|
1.4716
|
0.4164
|
0.4077
| Mean |
1.5916
|
1.7878
|
1.9948
|
0.2550
|
0.2783
| 10% | | | | | | | |
6.7826
|
6.9083
|
6.9500
|
0.2450
|
0.2714
| |
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% | | |
0.0612
| | | | |
0.0159
|
−0.0189
|
0.0218
|
0.0400
|
0.0345
| |
0.0080
|
−0.0209
|
−0.0247
|
0.0462
|
0.0174
| Mean |
0.0145
|
0.0337
|
0.0308
|
0.0328
|
0.0192
| 5% | | | | | | | |
0.4342
|
0.4011
|
0.2954
|
0.0921
|
0.0921
| |
0.1110
|
0.1452
|
0.0526
|
0.0358
|
0.0073
| Mean |
0.2301
|
0.2310
|
0.1376
|
0.0490
|
0.0346
| 10% | | | | | | | |
0.9916
|
0.9875
|
0.96302
|
0.0793
|
0.0794
| |
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% | |
0.0226
|
0.0216
|
0.0240
|
−0.0505
| | |
−0.1086
|
−0.1037
|
−0.1099
|
−0.0514
|
−0.0457
| |
−0.0448
|
−0.0422
|
−0.0433
|
0.0371
|
0.0387
| Mean |
0.0587
|
0.0558
|
0.0591
|
0.0463
|
0.0466
| 5% | |
0.1218
|
0.1396
|
0.1095
|
0.0205
|
0.0048
| |
−0.1854
|
−0.3399
|
−0.2944
|
−0.1880
|
−0.1699
| |
−0.1944
|
−0.1522
|
−0.1174
|
−0.0163
|
−0.0038
| Mean |
0.1672
|
0.2106
|
0.1738
|
0.0749
|
0.0595
| 10% | |
0.7546
|
0.6492
|
0.8318
| | | |
−1.1835
|
−1.0402
|
−1.1809
|
0.3250
|
0.3294
| |
−0.8359
|
−0.7686
|
−1.0436
|
0.2800
|
0.2558
| Mean |
0.9247
|
0.8193
|
1.0187
|
0.2990
|
0.2867
|
|
|