| Table 1. Relative bias (RB%) of kNN and EDE estimators of totals in SRS (m = 1). RB% = (estimate – actual) / actual × 100. Results are for the k-value (kopt) that minimized the RMSE of an estimated total. | |||||||
| POP (kopt) | n | kNN | EDE | ||||
| Y1 | Y2 | Y3 | Y1 | Y2 | Y3 | ||
| POP1 (4) | 50 | –0.1 | 0.2 | 0.2 | –0.0 | 0.0 | 0.2 |
| 100 | –0.3 | –0.1 | –0.4 | 0.1 | –0.2 | –0.3 | |
| 200 | –0.4 | –0.1 | –0.3 | 0.0 | 0.0 | 0.3 | |
| 300 | –0.3 | 0.1 | –0.2 | 0.1 | 0.1 | –0.2 | |
| POP2 (8) | 50 | –0.8 | –0.2 | –0.4 | 0.3 | 0.4 | 0.4 |
| 100 | –0.6 | 0.3 | –0.5 | –0.3 | 0.1 | 0.2 | |
| 200 | –0.2 | 0.1 | –0.4 | 0.1 | 0.2 | –0.0 | |
| 300 | –0.1 | 0.2 | –0.3 | 0.1 | 0.1 | 0.1 | |
| POP3 (6) | 50 | 0.3 | 0.2 | 0.2 | 0.3 | 0.1 | 0.1 |
| 100 | 0.5 | 0.3 | 0.0 | 0.4 | 0.3 | 0.2 | |
| 200 | –0.4 | –0.2 | 0.3 | –0.1 | 0.0 | 0.2 | |
| 300 | –0.4 | 0.0 | 0.3 | 0.1 | 0.1 | –0.2 | |
| Table 2. Relative bias (RB%) of kNN and EDE estimators of totals in CLU (m = 4). RB% = (estimate – actual) / actual × 100. Results are for the k-value (kopt) that minimized the RMSE of an estimated total. | |||||||
| POP (kopt) | n | kNN | EDE | ||||
| Y1 | Y2 | Y3 | Y1 | Y2 | Y3 | ||
| POP1 (4) | 20 | –0.0 | 0.2 | 0.5 | 0.5 | 0.1 | 0.6 |
| 30 | –1.0 | –0.2 | –0.5 | –0.6 | –0.2 | –0.6 | |
| 50 | –0.5 | 0.1 | –0.3 | –0.1 | –0.3 | –0.1 | |
| 100 | –0.4 | –0.2 | –0.1 | –0.1 | –0.2 | –0.1 | |
| POP2 (6) | 20 | –0.4 | 0.6 | –0.3 | –0.1 | 0.6 | 0.2 |
| 30 | –0.1 | 0.0 | 0.3 | 0.2 | –0.1 | –0.0 | |
| 50 | –0.2 | –0.0 | 0.4 | –0.0 | –0.2 | –0.0 | |
| 100 | –0.2 | –0.0 | –0.4 | –0.1 | –0.2 | –0.1 | |
| POP3 (8) | 20 | –0.5 | –0.6 | 0.4 | –0.5 | –0.7 | 0.2 |
| 30 | –1.1 | –1.0 | 0.9 | –0.7 | –0.9 | 0.3 | |
| 50 | –0.4 | –0.2 | 0.6 | –0.1 | 0.0 | –0.1 | |
| 100 | –0.3 | 0.0 | 0.2 | 0.2 | 0.2 | –0.5 | |
| Table 3. Estimates of relative standard error (se%) in SRS. (se% = standard error of total ÷ total × 100). An estimate significantly different from its empirical counterpart at the 5% level (AD-test) is indicated in gray. | |||||||||||||
| Variance estimator | POP1 (kopt = 4) | POP2 (kopt = 8) | POP3 (kopt = 6) | ||||||||||
| n = | 50 | 100 | 200 | 300 | 50 | 100 | 200 | 300 | 50 | 100 | 200 | 300 | |
| vEMP | Y1 | 9.7 | 6.4 | 4.2 | 3.4 | 6.4 | 4.5 | 3.1 | 2.2 | 8.0 | 5.1 | 3.6 | 2.9 |
| Y2 | 9.2 | 6.0 | 4.0 | 3.4 | 7.0 | 4.4 | 3.2 | 2.5 | 8.0 | 5.5 | 3.7 | 3.0 | |
| Y3 | 9.8 | 6.9 | 5.0 | 3.8 | 5.8 | 3.7 | 2.8 | 2.1 | 9.5 | 6.2 | 4.2 | 3.3 | |
| vJK | Y1 | 9.7 | 6.6 | 4.6 | 3.6 | 6.9 | 4.6 | 3.1 | 2.4 | 7.9 | 5.4 | 3.7 | 3.0 |
| Y2 | 9.2 | 6.4 | 4.4 | 3.6 | 7.0 | 4.7 | 3.2 | 2.6 | 8.2 | 5.6 | 3.8 | 3.1 | |
| Y3 | 9.8 | 7.3 | 5.1 | 4.1 | 5.8 | 4.0 | 2.8 | 2.2 | 9.8 | 6.2 | 4.3 | 3.5 | |
| vBOOT | Y1 | 8.7 | 5.9 | 4.1 | 3.3 | 6.5 | 4.3 | 2.9 | 2.3 | 7.3 | 5.0 | 3.5 | 2.8 |
| Y2 | 8.4 | 5.8 | 4.0 | 3.2 | 6.5 | 4.5 | 3.0 | 2.4 | 7.6 | 5.1 | 3.6 | 2.9 | |
| Y3 | 9.5 | 6.6 | 4.6 | 3.7 | 6.4 | 3.7 | 2.6 | 2.1 | 8.1 | 5.7 | 4.0 | 3.2 | |
| vFBOOT | Y1 | 8.8 | 6.1 | 4.2 | 3.4 | 6.1 | 4.2 | 2.9 | 2.3 | 7.3 | 5.1 | 3.5 | 2.8 |
| Y2 | 8.8 | 6.0 | 4.2 | 3.4 | 6.4 | 4.5 | 3.0 | 2.4 | 7.6 | 5.2 | 3.6 | 2.9 | |
| Y3 | 9.7 | 6.7 | 4.8 | 3.8 | 6.1 | 3.7 | 2.6 | 2.1 | 8.2 | 5.8 | 4.1 | 3.3 | |
| vEDE | Y1 | 9.5 | 6.6 | 4.6 | 3.7 | 6.7 | 4.5 | 3.1 | 2.5 | 7.8 | 5.4 | 3.8 | 3.1 |
| Y2 | 9.3 | 6.4 | 4.5 | 3.7 | 6.8 | 4.6 | 3.2 | 2.6 | 8.0 | 5.5 | 3.9 | 3.0 | |
| Y3 | 10.6 | 7.3 | 5.1 | 4.1 | 6.0 | 4.1 | 2.9 | 2.3 | 9.8 | 6.2 | 4.3 | 3.5 | |
| Table 4. Estimates of relative standard error (se%) in CLU. (se% = standard error of total ÷ total × 100). An estimate significantly different from its empirical counterpart at the 5% level (AD-test) is indicated in gray. | |||||||||||||
| Variance estimator | POP1 (kopt = 4) | POP2 (kopt = 6) | POP3 (kopt = 8) | ||||||||||
| n = | 20 | 30 | 50 | 100 | 20 | 30 | 50 | 100 | 20 | 30 | 50 | 100 | |
| vEMP | Y1 | 8.2 | 6.3 | 5.0 | 3.4 | 5.2 | 4.2 | 3.0 | 2.2 | 6.3 | 5.0 | 3.7 | 2.4 |
| Y2 | 8.1 | 6.0 | 4.9 | 3.3 | 5.9 | 4.4 | 3.5 | 2.2 | 6.5 | 5.3 | 4.0 | 2.6 | |
| Y3 | 9.4 | 6.8 | 5.6 | 3.3 | 4.9 | 3.9 | 3.0 | 2.1 | 7.1 | 5.5 | 4.1 | 3.0 | |
| vJK | Y1 | 8.2 | 6.4 | 4.9 | 3.3 | 5.5 | 4.3 | 3.2 | 2.2 | 6.2 | 4.9 | 3.8 | 2.6 |
| Y2 | 8.0 | 6.4 | 4.8 | 3.3 | 5.7 | 4.6 | 3.4 | 2.3 | 6.4 | 5.2 | 3.9 | 2.7 | |
| Y3 | 8.9 | 7.0 | 5.4 | 3.7 | 4.9 | 3.9 | 3.0 | 2.1 | 7.2 | 5.7 | 4.4 | 3.1 | |
| vBOOT | Y1 | 7.7 | 6.1 | 4.7 | 3.2 | 5.1 | 4.1 | 3.0 | 2.1 | 5.7 | 4.7 | 3.6 | 2.5 |
| Y2 | 7.4 | 6.0 | 4.5 | 3.1 | 5.6 | 4.4 | 3.3 | 2.3 | 5.9 | 4.9 | 3.7 | 2.6 | |
| Y3 | 8.3 | 6.5 | 5.1 | 3.5 | 4.8 | 3.8 | 2.9 | 2.1 | 6.6 | 5.4 | 4.1 | 2.9 | |
| vFBOOT | Y1 | 7.7 | 6.1 | 4.6 | 3.2 | 5.0 | 4.0 | 3.0 | 2.0 | 5.7 | 4.7 | 3.6 | 2.5 |
| Y2 | 7.5 | 6.0 | 4.5 | 3.1 | 5.4 | 4.4 | 3.2 | 2.2 | 5.9 | 4.9 | 3.7 | 2.6 | |
| Y3 | 8.3 | 6.6 | 5.0 | 3.6 | 4.7 | 3.8 | 2.8 | 2.0 | 6.6 | 5.4 | 4.1 | 2.9 | |
| vEDE | Y1 | 8.3 | 6.6 | 5.1 | 3.5 | 5.4 | 4.4 | 3.3 | 2.2 | 6.1 | 5.0 | 3.8 | 2.6 |
| Y2 | 8.0 | 6.4 | 4.9 | 3.4 | 5.7 | 4.7 | 3.5 | 2.3 | 6.2 | 5.1 | 3.9 | 2.7 | |
| Y3 | 9.1 | 7.3 | 5.7 | 3.9 | 5.3 | 4.3 | 3.3 | 2.1 | 7.4 | 5.9 | 4.5 | 3.2 | |
| Table 5. Achieved coverage rates (%) of nominal 95% confidence intervals under SRS. Statistical significant (5% level) departures from the nominal level are in gray. | |||||||||||||
| Variance estimator | POP1 (kopt = 4) | POP2 (kopt = 8) | POP3 (kopt = 6) | ||||||||||
| n = | 50 | 100 | 200 | 300 | 50 | 100 | 200 | 300 | 50 | 100 | 200 | 300 | |
| vJK | Y1 | 95 | 95 | 96 | 95 | 95 | 95 | 95 | 97 | 95 | 95 | 97 | 97 |
| Y2 | 95 | 95 | 97 | 96 | 96 | 96 | 95 | 95 | 97 | 95 | 96 | 95 | |
| Y3 | 96 | 96 | 95 | 95 | 95 | 96 | 96 | 96 | 93 | 95 | 94 | 97 | |
| vBOOT | Y1 | 94 | 95 | 95 | 95 | 95 | 96 | 93 | 96 | 93 | 96 | 96 | 96 |
| Y2 | 93 | 95 | 97 | 93 | 95 | 95 | 95 | 96 | 97 | 95 | 96 | 93 | |
| Y3 | 96 | 94 | 95 | 94 | 94 | 96 | 95 | 95 | 93 | 96 | 94 | 96 | |
| vFBOOT | Y1 | 93 | 94 | 96 | 95 | 94 | 94 | 93 | 94 | 94 | 96 | 95 | 96 |
| Y2 | 94 | 95 | 96 | 93 | 94 | 96 | 93 | 94 | 96 | 94 | 95 | 96 | |
| Y3 | 96 | 94 | 95 | 94 | 93 | 95 | 95 | 94 | 94 | 94 | 93 | 96 | |
| vEDE | Y1 | 94 | 96 | 96 | 93 | 95 | 95 | 96 | 96 | 94 | 94 | 96 | 97 |
| Y2 | 95 | 94 | 97 | 94 | 95 | 95 | 95 | 94 | 96 | 95 | 94 | 93 | |
| Y3 | 95 | 95 | 94 | 95 | 94 | 95 | 94 | 95 | 92 | 94 | 96 | 95 | |
| Table 6. Achieved coverage rates (%) of nominal 95% confidence intervals under CLU. Statistical significant (5% level) departures from the nominal level are in gray. | |||||||||||||
| Variance estimator | POP1 (kopt = 4) | POP2 (kopt = 6) | POP3 (kopt = 8) | ||||||||||
| n = | 20 | 30 | 50 | 100 | 20 | 30 | 50 | 100 | 20 | 30 | 50 | 100 | |
| vJK | Y1 | 95 | 95 | 95 | 93 | 95 | 94 | 96 | 95 | 94 | 95 | 95 | 96 |
| Y2 | 94 | 95 | 93 | 96 | 94 | 97 | 95 | 96 | 96 | 94 | 93 | 96 | |
| Y3 | 93 | 95 | 94 | 97 | 94 | 95 | 95 | 94 | 95 | 96 | 96 | 96 | |
| vBOOT | Y1 | 94 | 94 | 94 | 93 | 94 | 95 | 96 | 95 | 92 | 95 | 95 | 97 |
| Y2 | 92 | 95 | 93 | 95 | 94 | 97 | 94 | 97 | 95 | 94 | 93 | 98 | |
| Y3 | 92 | 93 | 93 | 97 | 94 | 94 | 97 | 94 | 94 | 96 | 95 | 95 | |
| vFBOOT | Y1 | 93 | 94 | 94 | 94 | 93 | 93 | 93 | 93 | 93 | 95 | 96 | 96 |
| Y2 | 92 | 95 | 93 | 94 | 94 | 96 | 94 | 97 | 93 | 93 | 93 | 97 | |
| Y3 | 93 | 95 | 92 | 97 | 95 | 94 | 94 | 93 | 93 | 95 | 96 | 96 | |
| vEDE | Y1 | 95 | 96 | 96 | 93 | 94 | 93 | 96 | 93 | 93 | 96 | 95 | 96 |
| Y2 | 95 | 96 | 94 | 95 | 93 | 96 | 95 | 95 | 94 | 93 | 93 | 96 | |
| Y3 | 93 | 96 | 95 | 97 | 94 | 95 | 95 | 95 | 96 | 95 | 96 | 96 | |