Table 1 The evaluations of regression coefficients and redundancy parameters
From: M-test in linear models with negatively superadditive dependent errors
Estimates | n | LS | LAD | Huber | |||
|---|---|---|---|---|---|---|---|
I | II | I | II | I | II | ||
\(\hat{\beta}_{0}\) | 100 | 1.031 | 0.985 | 1.016 | 0.978 | 1.006 | 1.007 |
500 | 0.994 | 0.994 | 1.008 | 1.006 | 1.003 | 1.006 | |
1000 | 1.002 | 0.999 | 1.000 | 1.006 | 1.002 | 1.003 | |
\(\hat{\beta}_{1}\) | 100 | 1.983 | 2.008 | 1.992 | 2.016 | 2.131 | 2.131 |
500 | 2.003 | 2.011 | 1.997 | 2.003 | 1.996 | 1.992 | |
1000 | 1.997 | 1.997 | 1.999 | 1.998 | 1.996 | 1.994 | |
\(\hat{\sigma}^{2}_{n}\) | 100 | 12.764 | 12.671 | 0.984 | 0.987 | 9.095 | 9.100 |
500 | 12.965 | 12.941 | 0.997 | 0.997 | 9.193 | 9.206 | |
1000 | 12.967 | 12.956 | 0.998 | 0.998 | 9.208 | 9.291 | |
\(\hat{\lambda}_{n}\) | 100 | 1.000 | 1.000 | 0.282 | 0.282 | 0.825 | 0.825 |
500 | 1.000 | 1.000 | 0.241 | 0.241 | 0.822 | 0.823 | |
1000 | 1.000 | 1.000 | 0.233 | 0.234 | 0.822 | 0.821 | |