Table 3.
Comparison of MINQUE, MMINQUE, IAUE, MIAUE, REML and MREML estimators based on compound absolute bias, compound MSE and prop. negative values.
MMINQUE1 |
MMINQUE2 |
MINQUE |
MIAUE1 |
MIAUE2 |
IAUE |
REML |
MREML |
|||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Compound absolute bias | Compound MSE | Prop. negative values | Compound absolute bias | Compound MSE | Prop. negative values | Compound absolute bias | Compound MSE | Prop. negative values | Compound absolute bias | Compound MSE | Compound absolute bias | Compound MSE | Compound absolute bias | Compound MSE | Compound absolute bias | Compound MSE | Prop. negative values | Compound absolute bias | Compound MSE | |
P1 | ||||||||||||||||||||
V1 | 0.26 | 1.31 | 0.56 | 0.26 | 1.31 | 0.56 | 0.26 | 1.31 | 0.56 | 0.26 | 1.14 | 0.46 | 0.86 | 0.48 | 0.62 | 0.24 | 1.30 | 0.56 | 0.48 | 0.60 |
V2 | 2.35 | 71.58 | 0.52 | 2.35 | 71.58 | 0.52 | 2.35 | 71.58 | 0.52 | 2.28 | 70.70 | 3.87 | 50.51 | 4.15 | 50.48 | 2.16 | 69.84 | 0.52 | 4.27 | 37.20 |
V3 | 0.07 | 1.10 | 0.51 | 0.07 | 1.10 | 0.51 | 0.07 | 1.10 | 0.51 | 0.113 | 1.180 | 0.115 | 1.154 | 0.142 | 1.145 | 0.08 | 1.15 | 0.52 | 0.51 | 0.76 |
V4 | 2.38 | 78.14 | 0.46 | 2.38 | 78.14 | 0.46 | 2.38 | 78.14 | 0.46 | 1.95 | 69.88 | 3.49 | 53.12 | 3.75 | 52.82 | 2.03 | 77.22 | 0.46 | 3.63 | 40.47 |
V5 | 0.17 | 74.94 | 0.12 | 0.17 | 74.94 | 0.12 | 0.17 | 74.94 | 0.12 | 0.04 | 73.54 | 0.04 | 73.54 | 0.04 | 73.48 | 0.09 | 73.98 | 0.11 | 2.57 | 51.05 |
V6 | 0.16 | 72.47 | 0.45 | 0.16 | 72.47 | 0.45 | 0.16 | 72.47 | 0.45 | 1.31 | 74.07 | 2.01 | 74.64 | 1.99 | 74.62 | 0.16 | 59.58 | 0.45 | 3.05 | 43.37 |
P2 | ||||||||||||||||||||
V1 | 0.31 | 1.60 | 0.59 | 0.34 | 1.71 | 0.59 | 0.30 | 1.58 | 0.58 | 0.97 | 2.14 | 1.06 | 1.76 | 1.07 | 1.65 | 0.30 | 1.49 | 0.58 | 0.47 | 0.71 |
V2 | 2.46 | 73.83 | 0.51 | 2.64 | 76.98 | 0.50 | 2.48 | 75.08 | 0.50 | 2.35 | 72.49 | 3.83 | 52.10 | 4.03 | 47.80 | 2.30 | 71.62 | 0.51 | 4.62 | 39.94 |
V3 | 0.10 | 1.27 | 0.57 | 0.11 | 1.29 | 0.57 | 0.09 | 1.26 | 0.55 | 0.11 | 1.23 | 0.02 | 1.20 | 0.05 | 1.18 | 0.10 | 1.21 | 0.53 | 0.41 | 0.79 |
V4 | 1.88 | 77.52 | 0.45 | 2.16 | 85.20 | 0.46 | 1.86 | 78.37 | 0.45 | 2.10 | 72.07 | 3.51 | 59.58 | 3.81 | 55.81 | 2.06 | 71.80 | 0.46 | 3.92 | 39.09 |
V5 | 0.13 | 73.67 | 0.13 | 0.16 | 74.56 | 0.20 | 0.14 | 73.65 | 0.13 | 0.16 | 81.97 | 0.11 | 82.74 | 0.13 | 81.89 | 0.26 | 70.26 | 0.13 | 2.73 | 52.06 |
V6 | 0.13 | 71.18 | 0.46 | 0.18 | 71.46 | 0.49 | 0.13 | 71.68 | 0.45 | 1.17 | 70.60 | 1.17 | 70.64 | 1.18 | 70.60 | 0.20 | 62.32 | 0.45 | 2.82 | 44.62 |
P3 | ||||||||||||||||||||
V1 | 0.34 | 1.75 | 0.61 | 0.43 | 2.07 | 0.62 | 0.32 | 1.67 | 0.60 | 0.35 | 1.70 | 0.52 | 1.31 | 0.51 | 1.17 | 0.30 | 1.62 | 0.60 | 0.51 | 0.79 |
V2 | 2.13 | 71.98 | 0.53 | 2.73 | 84.52 | 0.53 | 2.11 | 74.92 | 0.52 | 2.37 | 75.17 | 4.07 | 57.85 | 4.22 | 51.77 | 2.16 | 72.28 | 0.52 | 4.58 | 39.35 |
V3 | 0.16 | 1.33 | 0.58 | 0.20 | 1.40 | 0.62 | 0.14 | 1.31 | 0.58 | 0.19 | 1.42 | 0.10 | 1.36 | 0.12 | 1.35 | 0.18 | 1.37 | 0.56 | 0.55 | 0.88 |
V4 | 1.90 | 83.40 | 0.49 | 2.44 | 98.91 | 0.51 | 1.87 | 85.07 | 0.49 | 2.22 | 79.91 | 3.58 | 63.87 | 3.72 | 57.87 | 2.10 | 76.30 | 0.47 | 4.04 | 42.02 |
V5 | 0.34 | 78.32 | 0.21 | 0.38 | 81.91 | 0.30 | 0.35 | 78.71 | 0.22 | 0.10 | 81.02 | 0.07 | 80.37 | 0.07 | 80.91 | 0.28 | 70.95 | 0.18 | 2.81 | 51.72 |
V6 | 0.31 | 72.42 | 0.49 | 0.43 | 72.52 | 0.53 | 0.32 | 73.06 | 0.50 | 0.53 | 69.95 | 0.45 | 70.24 | 0.49 | 69.96 | 0.37 | 65.51 | 0.47 | 2.97 | 48.21 |
P4 | ||||||||||||||||||||
V1 | 0.19 | 0.87 | 0.49 | 0.19 | 0.87 | 0.49 | 0.19 | 0.87 | 0.49 | 0.22 | 0.93 | 0.37 | 0.71 | 0.40 | 0.69 | 0.21 | 0.82 | 0.50 | 0.42 | 0.50 |
V2 | 1.74 | 47.46 | 0.52 | 1.74 | 47.46 | 0.52 | 1.74 | 47.46 | 0.52 | 1.97 | 50.14 | 3.23 | 33.67 | 3.57 | 33.94 | 1.60 | 44.45 | 0.51 | 4.01 | 27.32 |
V3 | 0.07 | 0.72 | 0.42 | 0.07 | 0.72 | 0.42 | 0.07 | 0.72 | 0.42 | 0.11 | 0.72 | 0.05 | 0.71 | 0.07 | 0.70 | 0.05 | 0.72 | 0.41 | 0.29 | 0.56 |
V4 | 1.55 | 49.22 | 0.41 | 1.55 | 49.22 | 0.41 | 1.55 | 49.22 | 0.41 | 1.82 | 50.21 | 2.44 | 35.56 | 2.80 | 35.21 | 1.52 | 50.01 | 0.42 | 3.42 | 29.36 |
V5 | 0.07 | 44.26 | 0.05 | 0.07 | 44.26 | 0.05 | 0.07 | 44.26 | 0.05 | 0.07 | 46.18 | 0.06 | 46.19 | 0.06 | 46.17 | 0.02 | 45.96 | 0.04 | 1.78 | 37.21 |
V6 | 0.08 | 41.14 | 0.40 | 0.08 | 41.14 | 0.40 | 0.08 | 41.14 | 0.40 | 0.12 | 40.03 | 0.06 | 40.02 | 0.08 | 40.03 | 0.12 | 38.72 | 0.40 | 2.15 | 31.08 |
P5 | ||||||||||||||||||||
V1 | 0.19 | 0.89 | 0.51 | 0.20 | 0.92 | 0.50 | 0.19 | 0.88 | 0.50 | 0.23 | 0.93 | 0.38 | 0.70 | 0.41 | 0.67 | 0.18 | 0.82 | 0.51 | 0.44 | 0.52 |
V2 | 1.81 | 48.00 | 0.50 | 1.91 | 49.65 | 0.49 | 1.81 | 48.16 | 0.50 | 1.93 | 46.84 | 3.40 | 33.10 | 3.74 | 32.83 | 1.60 | 46.59 | 0.50 | 4.02 | 28.13 |
V3 | 0.07 | 0.74 | 0.43 | 0.08 | 0.74 | 0.44 | 0.07 | 0.73 | 0.42 | 0.14 | 0.65 | 0.08 | 0.64 | 0.10 | 0.63 | 0.07 | 0.74 | 0.45 | 0.31 | 0.56 |
V4 | 1.52 | 49.82 | 0.43 | 1.60 | 51.85 | 0.43 | 1.54 | 50.18 | 0.43 | 1.79 | 48.26 | 3.00 | 36.57 | 3.37 | 35.86 | 1.55 | 52.40 | 0.44 | 3.43 | 30.87 |
V5 | 0.05 | 47.28 | 0.07 | 0.08 | 47.46 | 0.09 | 0.05 | 47.34 | 0.07 | 0.21 | 45.51 | 0.21 | 45.79 | 0.20 | 45.50 | 0.05 | 45.44 | 0.06 | 1.84 | 34.95 |
V6 | 0.15 | 39.08 | 0.41 | 0.15 | 39.28 | 0.44 | 0.16 | 39.13 | 0.40 | 0.26 | 42.02 | 0.20 | 42.07 | 0.22 | 42.02 | 0.16 | 34.61 | 0.40 | 2.03 | 34.78 |
P6 | ||||||||||||||||||||
V1 | 0.27 | 1.22 | 0.56 | 0.34 | 1.42 | 0.58 | 0.26 | 1.17 | 0.54 | 0.24 | 0.91 | 0.41 | 0.71 | 0.43 | 0.68 | 0.27 | 1.14 | 0.51 | 0.47 | 0.58 |
V2 | 2.01 | 52.2 | 0.51 | 2.4 | 60.76 | 0.5 | 1.97 | 53.47 | 0.51 | 2.07 | 45.43 | 3.53 | 33.59 | 3.83 | 32.92 | 1.81 | 48.7 | 0.5 | 4.05 | 29.28 |
V3 | 0.11 | 0.86 | 0.5 | 0.15 | 0.93 | 0.55 | 0.1 | 0.84 | 0.5 | 0.12 | 0.78 | 0.05 | 0.77 | 0.08 | 0.76 | 0.12 | 0.86 | 0.48 | 0.43 | 0.64 |
V4 | 1.85 | 50.84 | 0.42 | 2.17 | 58.89 | 0.44 | 1.92 | 52.13 | 0.41 | 1.74 | 28.59 | 1.74 | 50.89 | 4.99 | 47.00 | 1.48 | 68.84 | 0.43 | 5.48 | 43.34 |
V5 | 0.04 | 48.46 | 0.11 | 0.09 | 50.79 | 0.21 | 0.04 | 48.76 | 0.12 | 0.08 | 48.76 | 0.07 | 48.92 | 0.08 | 48.75 | 0.08 | 46.03 | 0.1 | 1.8 | 35.17 |
V6 | 0.38 | 43.31 | 0.46 | 0.48 | 43.41 | 0.48 | 0.39 | 43.58 | 0.48 | 0.19 | 43.45 | 0.16 | 43.46 | 0.16 | 43.46 | 0.32 | 41.36 | 0.44 | 2.17 | 33.22 |
P7 | ||||||||||||||||||||
V1 | 0.11 | 0.38 | 0.44 | 0.11 | 0.38 | 0.44 | 0.11 | 0.38 | 0.44 | 0.10 | 0.36 | 0.17 | 0.31 | 0.19 | 0.31 | 0.12 | 0.40 | 0.42 | 0.21 | 0.28 |
V2 | 0.96 | 18.95 | 0.53 | 0.96 | 18.95 | 0.53 | 0.96 | 18.95 | 0.53 | 1.20 | 18.84 | 1.94 | 15.42 | 2.17 | 15.58 | 0.96 | 19.54 | 0.52 | 2.43 | 14.22 |
V3 | 0.02 | 0.49 | 0.33 | 0.02 | 0.49 | 0.33 | 0.02 | 0.49 | 0.33 | 0.08 | 0.51 | 0.03 | 0.50 | 0.05 | 0.50 | 0.05 | 0.51 | 0.31 | 0.26 | 0.42 |
V4 | 0.79 | 22.14 | 0.41 | 0.79 | 22.14 | 0.41 | 0.79 | 22.14 | 0.41 | 0.81 | 20.43 | 1.85 | 17.60 | 2.09 | 17.44 | 0.77 | 21.33 | 0.39 | 1.6 | 14.65 |
V5 | 0.15 | 40.31 | 0.02 | 0.15 | 40.31 | 0.02 | 0.15 | 40.31 | 0.02 | 0.07 | 38.37 | 0.13 | 38.37 | 0.13 | 38.37 | 0.01 | 37.67 | 0.01 | 1.5 | 29.98 |
V6 | 0.06 | 33.64 | 0.31 | 0.06 | 33.64 | 0.31 | 0.06 | 33.64 | 0.31 | 0.26 | 33.32 | 0.25 | 33.31 | 0.28 | 33.31 | 0.05 | 34.64 | 0.30 | 1.43 | 27.34 |
P8 | ||||||||||||||||||||
V1 | 0.10 | 0.42 | 0.44 | 0.11 | 0.43 | 0.44 | 0.10 | 0.41 | 0.45 | 0.12 | 0.39 | 0.21 | 0.34 | 0.23 | 0.33 | 0.11 | 0.42 | 0.42 | 0.25 | 0.29 |
V2 | 0.87 | 18.82 | 0.53 | 0.92 | 19.26 | 0.52 | 0.87 | 19.15 | 0.52 | 1.08 | 18.47 | 2.39 | 15.52 | 2.59 | 15.33 | 0.93 | 19.12 | 0.51 | 2.37 | 13.74 |
V3 | 0.05 | 0.52 | 0.33 | 0.05 | 0.51 | 0.34 | 0.05 | 0.52 | 0.32 | 0.09 | 0.50 | 0.01 | 0.49 | 0.04 | 0.49 | 0.04 | 0.54 | 0.30 | 0.26 | 0.45 |
V4 | 0.68 | 20.07 | 0.4 | 0.74 | 20.7 | 0.41 | 0.68 | 20.44 | 0.4 | 0.91 | 21.43 | 1.76 | 18.74 | 2.01 | 18.06 | 0.5 | 21.23 | 0.40 | 1.71 | 14.52 |
V5 | 0.02 | 37.66 | 0.01 | 0.02 | 37.74 | 0.01 | 0.02 | 37.7 | 0.01 | 0.14 | 35.13 | 0.19 | 35.10 | 0.20 | 35.12 | 0.12 | 35.91 | 0.01 | 1.61 | 29.0 |
V6 | 0.1 | 35.23 | 0.32 | 0.11 | 35.19 | 0.35 | 0.10 | 35.3 | 0.31 | 0.05 | 35.41 | 0.06 | 35.40 | 0.07 | 35.41 | 0.04 | 33.19 | 0.29 | 1.55 | 26.66 |
P9 | ||||||||||||||||||||
V1 | 0.11 | 0.48 | 0.45 | 0.14 | 0.53 | 0.46 | 0.11 | 0.46 | 0.45 | 0.14 | 0.46 | 0.25 | 0.41 | 0.26 | 0.37 | 0.11 | 0.45 | 0.42 | 0.25 | 0.31 |
V2 | 1.02 | 20.63 | 0.51 | 1.25 | 22.64 | 0.5 | 1.05 | 22.22 | 0.51 | 1.23 | 18.97 | 2.62 | 17.27 | 2.76 | 16.18 | 0.9 | 20.14 | 0.51 | 2.41 | 14.77 |
V3 | 0.08 | 0.61 | 0.38 | 0.09 | 0.6 | 0.4 | 0.07 | 0.60 | 0.36 | 0.11 | 0.55 | 0.03 | 0.53 | 0.07 | 0.54 | 0.05 | 0.57 | 0.32 | 0.28 | 0.46 |
V4 | 0.75 | 22.45 | 0.41 | 0.98 | 25.13 | 0.42 | 0.74 | 23.91 | 0.41 | 0.91 | 23.35 | 1.99 | 21.65 | 2.14 | 19.51 | 0.74 | 21.8 | 0.37 | 1.73 | 15.0 |
V5 | 0.11 | 35.74 | 0.01 | 0.10 | 36.54 | 0.03 | 0.10 | 35.95 | 0.02 | 0.03 | 36.21 | 0.10 | 36.98 | 0.11 | 36.20 | 0.02 | 38.19 | 0.01 | 1.54 | 30.42 |
V6 | 0.22 | 34.73 | 0.37 | 0.25 | 34.86 | 0.41 | 0.21 | 34.86 | 0.36 | 0.17 | 33.34 | 0.17 | 33.26 | 0.19 | 33.33 | 0.14 | 35.54 | 0.32 | 1.49 | 28.09 |