Table 1. Root Mean Squared Error (RMSE) of slope estimators (sample size = 50; number of samples =
500). Source: McDonald and White (1993).
|
Underlying Error-Term |
Underlying Error-Term | ||||||
|
Estimation Technique |
Normal |
Normal Mixture |
Log- Normal |
Estimation Technique |
Normal |
Normal Mixture |
Log- Normal |
|
OLS |
0.28 |
0.28 |
0.28 |
Huber 1, c=1 |
0.29 |
0.14 |
0.16 |
|
LAD |
0.35 |
0.13 |
0.17 |
Huber 1, c=1.5 |
0.28 |
0.16 |
0.18 |
|
BT |
0.29 |
0.14 |
0.18 |
Huber 1, c=2 |
0.28 |
0.19 |
0.20 |
|
GT |
0.30 |
0.12 |
0.12 |
Huber 2 c=1 |
0.56 |
0.12 |
0.12 |
|
T |
0.28 |
0.11 |
0.12 |
Huber 2 c=1.5 |
0.41 |
0.11 |
0.15 |
|
BT, p≥1 |
0.29 |
0.13 |
0.17 |
Huber 2 c=2 |
0.32 |
0.13 |
0.16 |
|
GT, p≥1 |
0.30 |
0.12 |
0.12 |
Manski (AML) |
0.28 |
0.12 |
0.13 |
|
EGB2(p=q) |
0.28 |
0.12 |
0.15 |
Newey (j) |
0.30 |
0.12 |
0.11 |
|
EGB2 |
0.29 |
0.12 |
0.05 |
Proposed |
0.28 |
0.11 |
0.05 |
Notes: OLS is the Ordinary Least Squares estimator; LAD is the Least Absolute Deviations estimator
(Gentle, 1997); BT is the power exponential or Box-Tiao estimator (Zeckhauser and Thompson, 1970), GT
is a partially adaptive estimator based on the generalized t distribution (McDonald and Newey, 1984,
1988); t is a partially adaptive estimator based on the Student’s t distribution; EGB2 is a partially adaptive
estimator based on the exponential generalized beta distribution of the second kind; Huber 1 and 2 refer to
the estimators proposed by Huber (1964) and Huber (1981); Manski (AML) is the adaptive maximum
likelihood estimator advanced by Hsieh and Manski (1987) based on a normal kernel density; and Newey
(j) is the generalized method of moments estimator with j moments used in estimation (Newey, 1988). For
more details about the former estimation techniques please see McDonald and White (1993).
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