Table 4.
Efficiency of TPS relative to various alternative estimators for estimating V E(S(1)).
| γwv | γsv | γwp | γsp | V E(s0.1)* | VE(s0.3)* | VE(s0.5)* | V E(s0.7)* | V E(s0.9)* | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TPS | TEL | WPS | WEL | TPS | TEL | WPS | WEL | TPS | TEL | WPS | WEL | TPS | TEL | WPS | WEL | TPS | TEL | WPS | WEL | ||||
| BIP-only Design | |||||||||||||||||||||||
| 1 | 1 | 1 | 0 | 1.00 | 1.05 | 1.69 | 1.89 | 1.00 | 1.02 | 1.31 | 1.36 | 1.00 | 1.03 | 1.11 | 1.15 | 1.00 | 1.07 | 1.56 | 1.90 | 1.00 | 1.00 | 2.19 | 7.14 |
| 1 | 1 | 5 | 0 | 1.00 | 1.04 | 1.14 | 1.14 | 1.00 | 1.02 | 1.08 | 1.09 | 1.00 | 1.01 | 1.01 | 1.01 | 1.00 | 1.03 | 1.05 | 1.05 | 1.00 | 1.02 | 1.02 | 1.03 |
| 1 | 1 | 10 | 0 | 1.00 | 1.06 | 1.16 | 1.16 | 1.00 | 1.02 | 1.07 | 1.07 | 1.00 | 1.01 | 1.01 | 1.01 | 1.00 | 1.03 | 1.09 | 1.08 | 1.00 | 1.05 | 1.14 | 1.35 |
| 5 | 1 | 5 | 0 | 1.00 | 1.05 | 1.04 | 1.11 | 1.00 | 1.02 | 1.03 | 1.06 | 1.00 | 1.01 | 1.00 | 1.02 | 1.00 | 1.03 | 1.00 | 1.04 | 1.00 | 1.03 | 0.99 | 1.05 |
| 10 | 1 | 10 | 0 | 1.00 | 1.06 | 1.00 | 1.06 | 1.00 | 1.02 | 1.00 | 1.02 | 1.00 | 1.02 | 1.00 | 1.02 | 1.00 | 1.09 | 1.00 | 1.08 | 1.00 | 1.26 | 1.00 | 1.22 |
| 2 | 2 | 2 | 0 | 1.00 | 0.95 | 1.23 | 1.23 | 1.00 | 0.98 | 1.11 | 1.11 | 1.00 | 1.00 | 1.01 | 1.02 | 1.00 | 0.99 | 1.11 | 1.11 | 1.00 | 0.98 | 1.18 | 1.20 |
| 2 | 2 | 5 | 0 | 1.00 | 0.97 | 1.04 | 1.04 | 1.00 | 0.99 | 1.04 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.01 |
| 2 | 2 | 10 | 0 | 1.00 | 1.01 | 1.06 | 1.05 | 1.00 | 1.00 | 1.02 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.01 | 1.02 | 1.01 | 1.00 | 1.01 | 1.04 | 1.02 |
| 5 | 5 | 2 | 0 | 1.00 | 0.98 | 1.29 | 1.29 | 1.00 | 0.99 | 1.11 | 1.11 | 1.00 | 1.01 | 1.02 | 1.03 | 1.00 | 1.01 | 1.17 | 1.18 | 1.00 | 1.01 | 1.37 | 1.42 |
| 5 | 5 | 5 | 0 | 1.00 | 0.97 | 1.04 | 1.04 | 1.00 | 0.99 | 1.02 | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.98 | 1.01 | 1.01 | 1.00 | 0.97 | 1.01 | 1.01 |
| 5 | 5 | 10 | 0 | 1.00 | 0.99 | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| 10 | 10 | 10 | 0 | 1.00 | 1.00 | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 |
| BIP+CPV Design | |||||||||||||||||||||||
| 1 | 1 | 1 | 1 | 1.00 | 1.28 | 45.86 | 136.21 | 1.00 | 1.11 | 4.31 | 8.76 | 1.00 | 1.11 | 2.36 | 3.58 | 1.00 | 1.53 | 12.36 | 21.74 | 1.00 | 5.55 | 473.59 | 872.24 |
| 1 | 1 | 5 | 5 | 1.00 | 2.19 | 2.08 | 13.60 | 1.00 | 1.46 | 1.47 | 3.63 | 1.00 | 1.13 | 1.06 | 1.70 | 1.00 | 1.61 | 1.46 | 4.89 | 1.00 | 2.24 | 2.06 | 33.91 |
| 1 | 1 | 10 | 10 | 1.00 | 4.00 | 1.72 | 6.82 | 1.00 | 2.04 | 1.32 | 2.82 | 1.00 | 1.75 | 1.03 | 2.05 | 1.00 | 8.32 | 1.24 | 11.64 | 1.00 | 454.01 | 1.47 | 715.07 |
| 5 | 1 | 5 | 1 | 1.00 | 1.20 | 1.12 | 1.61 | 1.00 | 1.08 | 1.05 | 1.25 | 1.00 | 1.04 | 1.01 | 1.10 | 1.00 | 1.14 | 1.05 | 1.44 | 1.00 | 1.22 | 1.10 | 2.27 |
| 10 | 1 | 10 | 1 | 1.00 | 1.20 | 1.01 | 1.28 | 1.00 | 1.08 | 1.00 | 1.11 | 1.00 | 1.04 | 1.00 | 1.05 | 1.00 | 1.19 | 1.01 | 1.25 | 1.00 | 1.57 | 1.01 | 1.83 |
| 2 | 2 | 2 | 2 | 1.00 | 1.11 | 2.76 | 49.45 | 1.00 | 1.04 | 1.58 | 3.42 | 1.00 | 1.02 | 1.18 | 1.74 | 1.00 | 1.08 | 2.23 | 6.82 | 1.00 | 1.16 | 6.54 | 227.20 |
| 2 | 2 | 5 | 5 | 1.00 | 1.33 | 1.47 | 2.91 | 1.00 | 1.12 | 1.21 | 1.67 | 1.00 | 1.04 | 1.03 | 1.19 | 1.00 | 1.19 | 1.23 | 2.07 | 1.00 | 1.34 | 1.52 | 4.00 |
| 2 | 2 | 10 | 10 | 1.00 | 1.94 | 1.27 | 2.69 | 1.00 | 1.33 | 1.11 | 1.58 | 1.00 | 1.11 | 1.01 | 1.20 | 1.00 | 1.62 | 1.11 | 2.23 | 1.00 | 3.21 | 1.21 | 9.14 |
| 5 | 5 | 2 | 2 | 1.00 | 1.03 | 2.21 | 3.17 | 1.00 | 1.01 | 1.39 | 1.60 | 1.00 | 1.01 | 1.17 | 1.28 | 1.00 | 1.02 | 2.36 | 3.30 | 1.00 | 1.04 | 20.40 | 60.57 |
| 5 | 5 | 5 | 5 | 1.00 | 1.06 | 1.24 | 1.66 | 1.00 | 1.02 | 1.09 | 1.23 | 1.00 | 1.01 | 1.01 | 1.05 | 1.00 | 1.04 | 1.12 | 1.36 | 1.00 | 1.07 | 1.26 | 1.80 |
| 5 | 5 | 10 | 10 | 1.00 | 1.24 | 1.07 | 1.47 | 1.00 | 1.08 | 1.03 | 1.15 | 1.00 | 1.02 | 1.00 | 1.04 | 1.00 | 1.12 | 1.04 | 1.24 | 1.00 | 1.23 | 1.07 | 1.48 |
| 10 | 10 | 10 | 10 | 1.00 | 1.06 | 1.03 | 1.17 | 1.00 | 1.02 | 1.01 | 1.05 | 1.00 | 1.01 | 1.00 | 1.02 | 1.00 | 1.04 | 1.02 | 1.11 | 1.00 | 1.08 | 1.04 | 1.21 |
Efficiency of TPS relative to estimator A = variance of A/variance of TPS.
V E(sα)* is V E(s) for s the α × 100% percentile of S(1).