Robust Bayesian Regularized Estimation Based on Regression Model

Table 1

Simulation results of MMAD for different distribution errors.

Method					Normal mixture	Laplace mixture
Simulation 1
BAT.L	0.2321 (0.1211)	1.0274 (0.4014)	0.3012 (0.1287)	0.2721 (0.2201)	0.3734 (0.4105)	0.4168 (0.3710)
BLS.L	0.3613 (0.1068)	0.9694 (0.3339)	0.4980 (0.2126)	0.4958 (0.1556)	0.8623 (0.3160)	0.8498 (0.5587)
BALS.L	0.2147 (0.1145)	0.9433 (0.4071)	0.3517 (0.2010)	0.3349 (0.1770)	0.7209 (0.3799)	0.6407 (0.6589)
LASSO	0.3221 (0.1311)	0.9755 (0.4875)	0.4396 (0.2771)	0.4306 (0.1635)	0.8073 (0.3775)	0.7993 (0.5934)
ALASSO	0.2219 (0.1165)	0.9609 (0.4882)	0.3504 (0.2628)	0.3265 (0.1962)	0.8352 (0.4046)	0.6840 (0.6998)
Simulation 2
BAT.L	0.1362 (0.0658)	0.3932 (0.2607)	0.2188 (0.1658)	0.1745 (0.0906)	0.2587 (0.2985)	0.2330 (0.1060)
BLS.L	0.3081 (0.0877)	0.6778 (0.2811)	0.4881 (0.2249)	0.4709 (0.1606)	0.7045 (0.2552)	0.7356 (0.2784)
BALS.L	0.1308 (0.1100)	0.4518 (0.3194)	0.2479 (0.2349)	0.2015 (0.1759)	0.3700 (0.2961)	0.4355 (0.2568)
LASSO	0.1910 (0.1089)	0.6835 (0.3459)	0.3506 (0.2245)	0.3112 (0.1935)	0.5540 (0.3064)	0.4977 (0.3626)
ALASSO	0.0932 (0.1219)	0.4152 (0.3220)	0.2187 (0.2509)	0.1508 (0.2113)	0.2429 (0.3322)	0.3974 (0.3141)
Simulation 3
BAT.L	0.3253 (0.1049)	0.8987 (0.4659)	0.3108 (0.1538)	0.3610 (0.3654)	0.3915 (0.1939)	0.4196 (0.0112)
BLS.L	0.6694 (0.1443)	1.7382 (0.3742)	0.8894 (0.3500)	0.9042 (0.2057)	1.6136 (0.6524)	1.3718 (0.0775)
BALS.L	0.3183 (0.1374)	0.9895 (0.3686)	0.5150 (0.2234)	0.4676 (0.1962)	0.9364 (0.5522)	0.6973 (0.0660)
LASSO	0.4469 (0.1449)	1.3959 (0.4807)	0.7231 (0.3199)	0.6462 (0.2530)	1.2599 (0.6710)	1.1223 (0.1315)
ALASSO	0.2803 (0.1463)	0.9267 (0.4087)	0.4601 (0.2306)	0.4513 (0.2290)	0.9204 (0.8101)	0.6814 (0.0987)

In the parentheses are standard deviations of the MMADs obtained 500 bootstrap resampling. The bold numbers correspond to the smallest MMAD in each category.