Table 4.
Estimated median of the point estimates of γ, CP (in %), ML (in %), MR (in %), Ratio (ML/(ML + MR)), DP (in %) and EP (in %) of two-sided 95% CIs of γ for the LR, Fieller’s and delta methods against γ, with a = 0.1 and 0.3, p = 0.1 and 0.3, n = 2,000 and ρ = 0 based on 10,000 replicates
| LR | Fieller | Deltaa | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a | p | γ | Median | CP | ML | MR | Ratio | DP | EP | CP | ML | MR | Ratio | DP | EP | CP | ML | MR | Ratio |
| 0.1 | 0.1 | 0 | 0.00 | 94.78 | 2.70 | 0.00 | 1.00 | 1.22 | 2.16 | 94.90 | 2.60 | 0.00 | 1.00 | 1.12 | 2.13 | 99.36 | 0.64 | 0.00 | 1.00 |
| 0.1 | 0.1 | 0.5 | 0.49 | 94.94 | 2.17 | 2.68 | 0.45 | 0.00 | 0.00 | 95.01 | 2.12 | 2.69 | 0.44 | 0.00 | 0.00 | 93.57 | 0.00 | 6.43 | 0.00 |
| 0.1 | 0.1 | 1 | 1.00 | 95.07 | 2.12 | 2.40 | 0.47 | 0.00 | 0.05 | 95.03 | 2.13 | 2.42 | 0.47 | 0.00 | 0.07 | 91.37 | 0.00 | 8.63 | 0.00 |
| 0.1 | 0.1 | 1.5 | 1.48 | 94.95 | 1.89 | 2.56 | 0.42 | 0.00 | 0.44 | 94.97 | 1.91 | 2.52 | 0.43 | 0.00 | 0.44 | 90.72 | 0.00 | 9.28 | 0.00 |
| 0.1 | 0.1 | 2 | 1.99 | 95.07 | 0.00 | 2.61 | 0.00 | 0.00 | 2.31 | 95.08 | 0.00 | 2.63 | 0.00 | 0.00 | 2.29 | 90.50 | 0.00 | 9.50 | 0.00 |
| 0.1 | 0.3 | 0 | 0.00 | 95.15 | 2.40 | 0.00 | 1.00 | 0.00 | 2.44 | 95.05 | 2.46 | 0.00 | 1.00 | 0.00 | 2.49 | 97.12 | 2.88 | 0.00 | 1.00 |
| 0.1 | 0.3 | 0.5 | 0.50 | 94.83 | 2.61 | 2.56 | 0.50 | 0.00 | 0.00 | 94.86 | 2.56 | 2.58 | 0.50 | 0.00 | 0.00 | 95.65 | 1.68 | 2.67 | 0.39 |
| 0.1 | 0.3 | 1 | 1.00 | 95.18 | 2.46 | 2.34 | 0.51 | 0.00 | 0.00 | 95.20 | 2.47 | 2.33 | 0.51 | 0.00 | 0.00 | 95.86 | 0.54 | 3.60 | 0.13 |
| 0.1 | 0.3 | 1.5 | 1.50 | 94.66 | 2.65 | 2.69 | 0.50 | 0.00 | 0.00 | 94.70 | 2.65 | 2.65 | 0.50 | 0.00 | 0.00 | 95.50 | 0.00 | 4.50 | 0.00 |
| 0.1 | 0.3 | 2 | 2.00 | 94.90 | 0.00 | 2.47 | 0.00 | 0.00 | 2.62 | 94.88 | 0.00 | 2.49 | 0.00 | 0.00 | 2.63 | 95.31 | 0.00 | 4.69 | 0.00 |
| 0.3 | 0.1 | 0 | 0.00 | 94.70 | 2.88 | 0.00 | 1.00 | 0.98 | 2.01 | 94.79 | 2.83 | 0.00 | 1.00 | 1.01 | 1.99 | 99.43 | 0.57 | 0.00 | 1.00 |
| 0.3 | 0.1 | 0.5 | 0.49 | 94.79 | 2.45 | 2.53 | 0.49 | 0.00 | 0.00 | 94.69 | 2.45 | 2.55 | 0.49 | 0.00 | 0.00 | 93.73 | 0.00 | 6.27 | 0.00 |
| 0.3 | 0.1 | 1 | 0.99 | 94.89 | 2.05 | 2.50 | 0.45 | 0.00 | 0.10 | 94.95 | 2.03 | 2.46 | 0.45 | 0.00 | 0.10 | 91.56 | 0.00 | 8.44 | 0.00 |
| 0.3 | 0.1 | 1.5 | 1.50 | 95.03 | 1.80 | 2.50 | 0.42 | 0.00 | 0.37 | 95.09 | 1.78 | 2.47 | 0.42 | 0.00 | 0.37 | 91.16 | 0.00 | 8.84 | 0.00 |
| 0.3 | 0.1 | 2 | 1.98 | 95.17 | 0.00 | 2.28 | 0.00 | 0.00 | 2.55 | 95.17 | 0.00 | 2.25 | 0.00 | 0.00 | 2.58 | 90.80 | 0.00 | 9.20 | 0.00 |
| 0.3 | 0.3 | 0 | 0.00 | 94.85 | 2.50 | 0.00 | 1.00 | 0.00 | 2.61 | 94.82 | 2.56 | 0.00 | 1.00 | 0.00 | 2.62 | 97.03 | 2.97 | 0.00 | 1.00 |
| 0.3 | 0.3 | 0.5 | 0.50 | 95.16 | 2.38 | 2.17 | 0.52 | 0.00 | 0.00 | 95.11 | 2.42 | 2.17 | 0.53 | 0.00 | 0.00 | 96.21 | 1.56 | 2.23 | 0.41 |
| 0.3 | 0.3 | 1 | 1.00 | 94.98 | 2.47 | 2.55 | 0.49 | 0.00 | 0.00 | 94.99 | 2.45 | 2.56 | 0.49 | 0.00 | 0.00 | 95.66 | 0.66 | 3.68 | 0.15 |
| 0.3 | 0.3 | 1.5 | 1.50 | 94.76 | 2.68 | 2.56 | 0.51 | 0.00 | 0.00 | 94.78 | 2.70 | 2.52 | 0.52 | 0.00 | 0.00 | 95.48 | 0.00 | 4.52 | 0.00 |
| 0.3 | 0.3 | 2 | 2.00 | 94.80 | 0.00 | 2.55 | 0.00 | 0.00 | 2.65 | 94.79 | 0.00 | 2.55 | 0.00 | 0.00 | 2.66 | 95.19 | 0.00 | 4.81 | 0.00 |
a DP and EP of the delta method are zero