Theory and Modern Applications
Table 1 The means, medians, and standard deviations of estimators
a = −0.2, b = 0.4 | a = −0.2, b = 0.5 | a = −0.2, b = 0.6 | |
|---|---|---|---|
Panel 1. Low parameter value θ = 0.8000 | |||
Mean (\(\hat{\theta}_{n}\)) | 0.6109 | 0.7290 | 0.7544 |
Median (\(\hat{\theta}_{n}\)) | 0.8029 | 0.8185 | 0.8247 |
Std. dev. (\(\hat{\theta}_{n}\)) | 0.5560 | 0.3874 | 0.3370 |
Mean (\(\check{\theta}_{n}\)) | 0.7741 | 0.7967 | 0.7921 |
Median (\(\check{\theta}_{n}\)) | 0.8407 | 0.8374 | 0.8339 |
Std. dev. (\(\check{\theta}_{n}\)) | 0.2917 | 0.2568 | 0.3061 |
Panel 2. Medium parameter value θ = 1.6931 | |||
Mean (\(\hat{\theta}_{n}\)) | 1.5894 | 1.6275 | 1.6262 |
Median (\(\hat{\theta}_{n}\)) | 1.6865 | 1.6936 | 1.6919 |
Std. dev. (\(\hat{\theta}_{n}\)) | 0.4326 | 0.3594 | 0.3242 |
Mean (\(\check{\theta}_{n}\)) | 1.6430 | 1.6523 | 1.6424 |
Median (\(\check{\theta}_{n}\)) | 1.6931 | 1.6956 | 1.6940 |
Std. dev. (\(\check{\theta}_{n}\)) | 0.2529 | 0.2696 | 0.2739 |
Panel 3. High parameter value θ = 3.7097 | |||
Mean (\(\hat{\theta}_{n}\)) | 3.7004 | 3.7087 | 3.7093 |
Median (\(\hat{\theta}_{n}\)) | 3.7098 | 3.7097 | 3.7097 |
Std. dev. (\(\hat{\theta}_{n}\)) | 0.1967 | 0.0235 | 0.0182 |
Mean (\(\check{\theta}_{n}\)) | 3.7087 | 3.7103 | 3.7107 |
Median (\(\check{\theta}_{n}\)) | 3.7110 | 3.7110 | 3.7111 |
Std. dev. (\(\check{\theta}_{n}\)) | 0.1395 | 0.0299 | 0.0182 |