Table 1.
Squared bias BSQ, sample variance VAR, estimated variance EVAR and mean-squared error MSE for estimates of θ in the constant coefficient of variation model (2) as described in Section 7.1 when θ = 0.25†
| Estimator | Results for m = 3 |
Results for m = 9 |
||||||
|---|---|---|---|---|---|---|---|---|
| BSQ | VAR | EVAR | MSE | BSQ | VAR | EVAR | MSE | |
| θ= 0.25, n = 250 | ||||||||
| N–M | 2.84 | 3.63 | — | 6.47 | 0.42 | 0.92 | — | 1.34 |
| N–R | 47.45 | 4.21 | — | 51.66 | 9.18 | 1.33 | — | 10.51 |
| C–M | 0.09 | 5.05 | — | 5.13 | 0.00 | 1.02 | — | 1.02 |
| C–R | 0.60 | 17.78 | — | 18.38 | 0.00 | 2.24 | — | 2.24 |
| S–M | 0.03 | 4.91 | 5.00 | 4.95 | 0.00 | 1.01 | 1.24 | 1.01 |
| S–R | 9.18 | 9.27 | 8.83 | 18.45 | 0.19 | 2.09 | 2.23 | 2.28 |
| PS–M | 0.10 | 5.08 | 5.14 | 5.18 | 0.00 | 1.02 | 1.24 | 1.03 |
| PS–R | 0.32 | 12.00 | 11.90 | 12.32 | 0.00 | 2.28 | 2.35 | 2.28 |
| Semi–3 | 0.00 | 3.06 | 3.09 | 3.07 | 0.00 | 2.91 | 2.89 | 2.91 |
| Semi–2 | 0.01 | 4.89 | 5.02 | 4.90 | 0.01 | 5.63 | 5.43 | 5.64 |
| θ= 0.25, n = 500 | ||||||||
| N–M | 3.58 | 1.68 | — | 5.25 | 0.41 | 0.58 | — | 0.99 |
| N–R | 49.71 | 1.33 | — | 51.04 | 8.82 | 0.75 | — | 9.57 |
| C–M | 0.00 | 2.31 | — | 2.31 | 0.00 | 0.64 | — | 0.64 |
| C–R | 0.11 | 5.04 | — | 5.15 | 0.00 | 1.26 | — | 1.26 |
| S–M | 0.00 | 2.27 | 2.39 | 2.27 | 0.00 | 0.64 | 0.60 | 0.64 |
| S–R | 10.59 | 2.72 | 4.22 | 13.30 | 0.12 | 1.19 | 1.09 | 1.31 |
| PS–M | 0.00 | 2.32 | 2.45 | 2.32 | 0.00 | 0.64 | 0.60 | 0.64 |
| PS–R | 0.04 | 4.15 | 5.62 | 4.18 | 0.00 | 1.20 | 1.14 | 1.20 |
| Semi–3 | 0.00 | 1.59 | 1.55 | 1.59 | 0.00 | 1.53 | 1.45 | 1.53 |
| Semi–2 | 0.00 | 2.72 | 2.52 | 2.72 | 0.00 | 3.05 | 2.74 | 3.05 |
†
All quantities are multiplied by 10 000. The symbols ‘N’, ‘C’, ‘S’ and ‘PS’ refer to the naive, corrected, SIMEX and permutation SIMEX estimators respectively. ‘M’ and ‘R’ refer to moments and least square estimators. Semi–j is the semiparametric estimator partitioned into j groups.