Research Article
A Note on the Performance of Biased Estimators with Autocorrelated Errors
Table 2
Percent relative efficiency of the
class estimator over the PCTP estimator for
and
.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 0.1
| 0.1 | 2.11 | 1.86 | 1.69 | 1.79 | 1.60 | 1.46 | 0.64 | 0.59 | 0.55 | 0.85 | 0.73 | 0.65 | 0.73 | 0.63 | 0.57 | 0.29 | 0.26 | 0.24 | 0.5 | 1.28 | 1.13 | 1.02 | 1.08 | 0.96 | 0.89 | 0.39 | 0.36 | 0.33 | 0.51 | 0.44 | 0.39 | 0.44 | 0.38 | 0.34 | 0.18 | 0.16 | 0.15 | 0.9 | 0.44 | 0.39 | 0.36 | 0.38 | 0.34 | 0.31 | 0.13 | 0.12 | 0.12 | 0.18 | 0.15 | 0.14 | 0.15 | 0.13 | 0.12 | 0.06 | 0.05 | 0.05 | 0.5
| 0.1 | 2.17 | 1.93 | 1.74 | 1.85 | 1.65 | 1.51 | 0.67 | 0.61 | 0.57 | 0.88 | 0.76 | 0.67 | 0.76 | 0.66 | 0.59 | 0.31 | 0.27 | 0.25 | 0.5 | 1.73 | 1.53 | 1.39 | 1.47 | 1.31 | 1.20 | 0.53 | 0.48 | 0.45 | 0.70 | 0.60 | 0.53 | 0.60 | 0.52 | 0.47 | 0.24 | 0.22 | 0.20 | 0.9 | 1.29 | 1.14 | 1.03 | 1.09 | 0.97 | 0.89 | 0.39 | 0.36 | 0.33 | 0.52 | 0.44 | 0.39 | 0.44 | 0.38 | 0.34 | 0.18 | 0.16 | 0.15 | 0.9
| 0.1 | 2.24 | 1.98 | 1.80 | 1.90 | 1.70 | 1.56 | 0.69 | 0.63 | 0.59 | 0.92 | 0.79 | 0.70 | 0.78 | 0.68 | 0.61 | 0.32 | 0.28 | 0.26 | 0.5 | 2.18 | 1.93 | 1.75 | 1.85 | 1.65 | 1.52 | 0.67 | 0.61 | 0.57 | 0.88 | 0.76 | 0.68 | 0.76 | 0.66 | 0.59 | 0.31 | 0.27 | 0.25 | 0.9 | 2.11 | 1.87 | 1.69 | 1.79 | 1.60 | 1.47 | 0.64 | 0.59 | 0.55 | 0.85 | 0.73 | 0.65 | 0.73 | 0.63 | 0.57 | 0.29 | 0.26 | 0.24 | 2
| 0.1 | 2.41 | 2.14 | 1.94 | 2.05 | 1.84 | 1.70 | 0.76 | 0.69 | 0.65 | 1.00 | 0.86 | 0.77 | 0.86 | 0.75 | 0.67 | 0.35 | 0.31 | 0.29 | 0.5 | 3.35 | 2.98 | 2.70 | 2.86 | 2.56 | 2.35 | 1.04 | 0.95 | 0.90 | 1.38 | 1.19 | 1.06 | 1.18 | 1.03 | 0.92 | 0.48 | 0.43 | 0.39 | 0.9 | 4.33 | 3.83 | 3.47 | 3.67 | 3.28 | 3.02 | 1.33 | 1.22 | 1.14 | 1.76 | 1.52 | 1.35 | 1.51 | 1.31 | 1.17 | 0.61 | 0.55 | 0.50 |
| | 0.1
| 0.1 | 5.35 | 4.95 | 4.58 | 4.62 | 4.30 | 4.05 | 1.73 | 1.61 | 1.55 | 2.94 | 2.69 | 2.48 | 2.53 | 2.31 | 2.15 | 0.94 | 0.85 | 0.80 | 0.5 | 3.28 | 3.03 | 2.80 | 2.83 | 2.63 | 2.47 | 1.05 | 0.98 | 0.94 | 1.79 | 1.64 | 1.51 | 1.54 | 1.41 | 1.31 | 0.57 | 0.52 | 0.48 | 0.9 | 1.23 | 1.13 | 1.04 | 1.05 | 0.97 | 0.91 | 0.38 | 0.35 | 0.34 | 0.65 | 0.59 | 0.54 | 0.55 | 0.50 | 0.47 | 0.20 | 0.18 | 0.17 | 0.5
| 0.1 | 5.11 | 4.76 | 4.44 | 4.46 | 4.17 | 3.95 | 1.73 | 1.61 | 1.55 | 2.93 | 2.69 | 2.49 | 2.54 | 2.33 | 2.17 | 0.96 | 0.87 | 0.82 | 0.5 | 4.31 | 4.00 | 3.71 | 3.73 | 3.48 | 3.28 | 1.41 | 1.31 | 1.26 | 2.40 | 2.19 | 2.02 | 2.07 | 1.89 | 1.75 | 0.77 | 0.70 | 0.66 | 0.9 | 3.51 | 3.23 | 2.97 | 3.00 | 2.78 | 2.61 | 1.09 | 1.01 | 0.97 | 1.86 | 1.70 | 1.56 | 1.59 | 1.45 | 1.34 | 0.58 | 0.53 | 0.49 | 0.9
| 0.1 | 4.92 | 4.61 | 4.31 | 4.33 | 4.07 | 3.86 | 1.72 | 1.62 | 1.56 | 2.92 | 2.69 | 2.49 | 2.54 | 2.34 | 2.18 | 0.97 | 0.89 | 0.84 | 0.5 | 5.19 | 4.82 | 4.48 | 4.51 | 4.22 | 3.98 | 1.73 | 1.62 | 1.56 | 2.95 | 2.70 | 2.50 | 2.55 | 2.33 | 2.17 | 0.96 | 0.87 | 0.82 | 0.9 | 5.46 | 5.04 | 4.66 | 4.70 | 4.36 | 4.11 | 1.75 | 1.63 | 1.56 | 2.97 | 2.72 | 2.50 | 2.56 | 2.33 | 2.16 | 0.94 | 0.86 | 0.80 | 2
| 0.1 | 4.51 | 4.28 | 4.04 | 4.05 | 3.84 | 3.68 | 1.72 | 1.62 | 1.57 | 2.89 | 2.69 | 2.51 | 2.55 | 2.36 | 2.22 | 1.02 | 0.93 | 0.88 | 0.5 | 6.99 | 6.57 | 6.15 | 6.18 | 5.82 | 5.53 | 2.50 | 2.35 | 2.26 | 4.23 | 3.91 | 3.63 | 3.69 | 3.41 | 3.19 | 1.44 | 1.31 | 1.24 | 0.9 | 9.58 | 8.95 | 8.35 | 8.39 | 7.86 | 7.45 | 3.29 | 3.08 | 2.97 | 5.60 | 5.16 | 4.78 | 4.87 | 4.48 | 4.18 | 1.86 | 1.70 | 1.60 |
| | 0.1
| 0.1 | 4.82 | 4.74 | 4.46 | 4.52 | 4.44 | 4.32 | 2.38 | 2.31 | 2.34 | 3.98 | 3.99 | 3.85 | 3.73 | 3.64 | 3.51 | 1.80 | 1.67 | 1.61 | 0.5 | 3.39 | 3.30 | 3.08 | 3.13 | 3.04 | 2.94 | 1.57 | 1.51 | 1.52 | 2.61 | 2.60 | 2.50 | 2.43 | 2.35 | 2.26 | 1.14 | 1.05 | 1.01 | 0.9 | 2.01 | 1.90 | 1.73 | 1.78 | 1.68 | 1.59 | 0.76 | 0.72 | 0.72 | 1.28 | 1.24 | 1.16 | 1.14 | 1.08 | 1.02 | 0.48 | 0.44 | 0.42 | 0.5
| 0.1 | 3.14 | 3.16 | 3.03 | 3.05 | 3.05 | 3.02 | 1.82 | 1.80 | 1.84 | 3.03 | 3.10 | 3.05 | 2.92 | 2.91 | 2.85 | 1.56 | 1.47 | 1.43 | 0.5 | 3.92 | 3.84 | 3.60 | 3.65 | 3.57 | 3.46 | 1.90 | 1.84 | 1.86 | 3.16 | 3.17 | 3.06 | 2.96 | 2.89 | 2.79 | 1.44 | 1.34 | 1.29 | 0.9 | 4.69 | 4.50 | 4.15 | 4.24 | 4.08 | 3.90 | 1.97 | 1.88 | 1.88 | 3.29 | 3.23 | 3.07 | 3.00 | 2.87 | 2.74 | 1.32 | 1.21 | 1.15 | 0.9
| 0.1 | 2.47 | 2.50 | 2.42 | 2.42 | 2.44 | 2.43 | 1.52 | 1.52 | 1.56 | 2.52 | 2.61 | 2.59 | 2.47 | 2.48 | 2.45 | 1.40 | 1.33 | 1.30 | 0.5 | 4.13 | 4.06 | 3.83 | 3.87 | 3.80 | 3.70 | 2.07 | 2.02 | 2.05 | 3.46 | 3.49 | 3.38 | 3.26 | 3.20 | 3.11 | 1.65 | 1.54 | 1.49 | 0.9 | 5.78 | 5.60 | 5.22 | 5.31 | 5.15 | 4.97 | 2.62 | 2.53 | 2.54 | 4.39 | 4.36 | 4.18 | 4.06 | 3.93 | 3.78 | 1.90 | 1.75 | 1.68 | 2
| 0.1 | 1.77 | 1.79 | 1.74 | 1.74 | 1.76 | 1.75 | 1.14 | 1.14 | 1.18 | 1.88 | 1.96 | 1.96 | 1.86 | 1.89 | 1.89 | 1.13 | 1.09 | 1.08 | 0.5 | 4.36 | 4.30 | 4.08 | 4.11 | 4.07 | 3.98 | 2.30 | 2.26 | 2.31 | 3.83 | 3.91 | 3.83 | 3.67 | 3.64 | 3.57 | 1.98 | 1.87 | 1.82 | 0.9 | 6.93 | 6.81 | 6.41 | 6.49 | 6.38 | 6.21 | 3.48 | 3.39 | 3.45 | 5.82 | 5.88 | 5.72 | 5.51 | 5.42 | 5.28 | 2.83 | 2.65 | 2.57 |
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