Table 1 Summary of bias and standard deviation over 1000 simulations
From: \(L_{1}\)-Estimation for covariate-adjusted regression
n | Dist | Method | Bias (SD) | |||
|---|---|---|---|---|---|---|
\(\gamma _{0}\) | \(\gamma _{1}\) | \(\gamma _{2}\) | \(\gamma _{3}\) | |||
50 | Normal | LP | −0.0071 (0.0730) | 0.0003 (0.0093) | 0.0129 (0.0920) | 0.0003 (0.0130) |
\(L_{1}\) | −0.0083 (0.0767) | 0.0002 (0.0072) | 0.0134 (0.0939) | 0.0008 (0.0132) | ||
\(t_{3}\) | LP | 0.0114 (0.3651) | −0.0065 (0.1927) | 0.0027 (0.4083) | 0.0080 (0.3240) | |
\(L_{1}\) | 0.0213 (0.3566) | −0.0067 (0.1720) | 0.0070 (0.3969) | 0.0029 (0.3008) | ||
Cauchy | LP | 0.0946 (32.7370) | 0.8215 (35.8373) | −1.0257 (41.5098) | 1.3761 (32.1225) | |
\(L_{1}\) | −0.0861 (6.2061) | 0.4566 (7.0982) | −0.6856 (8.31108) | −0.0929 (3.1853) | ||
100 | Normal | LP | −0.0063 (0.0830) | 1.03e − 05 (0.0078) | 0.0116 (0.0685) | 0.0004 (0.0091) |
\(L_{1}\) | −0.0079 (0.0798) | 5.75e − 05 (0.0083) | 0.0080 (0.0762) | −0.0006 (0.0074) | ||
\(t_{3}\) | LP | −0.0249 (0.3126) | −0.0078 (0.0991) | 0.0078 (0.2443) | 0.0017 (0.1907) | |
\(L_{1}\) | −0.0297 (0.2964) | 0.0079 (0.0734) | 0.0093 (0.1890) | 0.0039 (0.1553) | ||
Cauchy | LP | 1.2813 (26.0130) | 0.4512 (20.6582) | −1.3174 (28.6553) | 0.6500 (14.6341) | |
\(L_{1}\) | 0.0733 (0.5163) | 0.0083 (0.1183) | 0.043 (0.7523) | −0.0147 (0.3702) | ||
200 | Normal | LP | −0.0007 (0.0376) | 3.87e − 05 (0.0027) | 0.0066 (0.0423) | −0.0002 (0.0043) |
\(L_{1}\) | −0.0024 (0.0383) | 4.56e − 05 (0.0024) | 0.0046 (0.0427) | 0.0005 (0.0041) | ||
\(t_{3}\) | LP | 0.0139 (0.2856) | −0.0029 (0.0648) | −0.0059 (0.1711) | 0.0015 (0.1347) | |
\(L_{1}\) | −0.0123 (0.1844) | −0.0035 (0.0502) | 0.0025 (0.1287) | 0.0023 (0.1195) | ||
Cauchy | LP | 1.7790 (23.2778) | −0.0714 (7.6870) | −1.1413 (20.6915) | −0.6269 (16.2315) | |
\(L_{1}\) | 0.0393 (0.2638) | −0.0030 (0.0678) | 0.0012 (0.1530) | 0.0059 (0.1407) | ||