Table 7 Parameter estimates and the 2-norm results between the parameter estimates and true values for the third example
Parameter | LS | WLS | bcWLS | Algorithm 2 | Algorithm 3 I | True value | |
|---|---|---|---|---|---|---|---|
\(\sigma_{m} = 0.005\) | \(\hat{\beta }_{1}\) | 4.2871 | 3.0437 | 3.0323 | 1.4492 | 1.6000 | 1.5 |
\(\hat{\beta }_{2}\) | 20.4395 | 20.1661 | 20.1635 | 19.6415 | 19.8517 | 20 | |
\(\hat{\beta }_{3}\) | 8.2360 | 9.1576 | 9.1653 | 10.4929 | 10.1000 | 10 | |
\(\hat{\beta }_{4}\) | − 5.4799 | − 4.8835 | − 4.8778 | − 4.1076 | − 4.0686 | − 4 | |
\(\left\| \Delta \varvec{\hat{\beta} } \right\|\) | 3.6419 | 1.9751 | 1.9601 | 0.6209 | 0.2161 | / | |
\(\sigma_{m} = 0.05\) | \(\hat{\beta }_{1}\) | 17.4372 | 10.6262 | 9.8311 | 1.6658 | 1.6000 | 1.5 |
\(\hat{\beta }_{2}\) | 23.1451 | 21.8015 | 21.5658 | 19.2789 | 20.1000 | 20 | |
\(\hat{\beta }_{3}\) | − 1.1115 | 3.8043 | 4.3941 | 10.4287 | 10.1000 | 10 | |
\(\hat{\beta }_{4}\) | − 12.0305 | − 8.7000 | − 8.3279 | − 4.0328 | − 4.2751 | − 4 | |
\(\left\| \Delta \varvec{\hat{\beta} } \right\|\) | 21.2566 | 12.1247 | 11.0461 | 0.8557 | 0.3251 | / | |
\(\sigma_{m} = 0.1\) | \(\hat{\beta }_{1}\) | 31.8167 | 14.5611 | 13.6686 | 1.6070 | 1.6000 | 1.5 |
\(\hat{\beta }_{2}\) | 26.2958 | 24.3009 | 23.8356 | 19.1696 | 20.1000 | 20 | |
\(\hat{\beta }_{3}\) | − 12.2376 | − 1.7409 | − 1.0338 | 9.7767 | 10.1000 | 10 | |
\(\hat{\beta }_{4}\) | − 18.4205 | − 1.7409 | − 8.9716 | − 3.2539 | − 4.1213 | − 4 | |
\(\left\| \Delta \varvec{\hat{\beta} } \right\|\) | 40.7579 | 18.8592 | 17.5854 | 1.1435 | 0.2115 | / | |