1. No category

Point estimate of MSE and its standard error in parentheses (multiplied by
100) based on 2000 replicates with n = 100 under four scenarios in Section 4.2
Table 1: Normal errors
q
Method
QR
WQR0.1
WQR0.3
WQR0.5
QR.M
WQR.M0.1
WQR.M0.3
WQR.M0.5
WQR.M20.1
WQR.M20.3
WQR.M20.5
0.1
20.55 (0.27)
20.17 (0.26)
19.63 (0.25)
19.44 (0.26)
20.11 (0.25)
19.60 (0.24)
18.70 (0.23)
18.01 (0.23)
19.46 (0.24)
18.44 (0.23)
17.95 (0.23)
0.25
12.25 (0.15)
12.04 (0.15)
11.71 (0.15)
11.56 (0.15)
10.64 (0.13)
10.38 (0.12)
9.98 (0.12)
9.74 (0.12)
10.30 (0.12)
9.83 (0.12)
9.59 (0.12)
0.5
10.11 (0.12)
9.78 (0.12)
9.40 (0.12)
9.16 (0.11)
8.42 (0.10)
8.18 (0.10)
7.80 (0.09)
7.53 (0.09)
8.07 (0.10)
7.55 (0.09)
7.21 (0.09)
0.8
14.11 (0.18)
13.79 (0.18)
13.40 (0.17)
13.28 (0.18)
12.54 (0.15)
12.25 (0.15)
11.80 (0.14)
11.53 (0.14)
12.17 (0.15)
11.64 (0.14)
11.40 (0.14)
NOTE: The subscript for weighted/scaled estimation methods (WQR, WQR.M and WQR.M2)
d ∗ + (1 − α), which determines
d ∗ = α · IQR
indicates the parameter α in the shrinkage estimate, IQR
i
i,α
weights/scales.
Table 2: Normal errors with 5% outliers mixed in, evaluated under the normal target
q
Method
QR
WQR0.1
WQR0.3
WQR0.5
QR.M
WQR.M0.1
WQR.M0.3
WQR.M0.5
WQR.M20.1
WQR.M20.3
WQR.M20.5
0.1
39.08 (0.68)
37.90 (0.65)
36.33 (0.62)
35.66 (0.61)
47.59 (0.89)
45.58 (0.83)
42.27 (0.75)
39.67 (0.70)
45.59 (0.83)
42.89 (0.77)
41.41 (0.75)
0.25
15.69 (0.20)
15.35 (0.20)
14.84 (0.19)
14.61 (0.20)
14.74 (0.18)
14.33 (0.18)
13.68 (0.18)
13.26 (0.18)
14.24 (0.18)
13.54 (0.17)
13.23 (0.17)
1
0.5
11.90 (0.15)
11.62 (0.14)
11.17 (0.14)
10.89 (0.14)
10.17 (0.12)
9.89 (0.12)
9.44 (0.11)
9.14 (0.11)
9.77 (0.12)
9.17 (0.11)
8.83 (0.11)
0.8
19.06 (0.26)
18.59 (0.25)
18.02 (0.25)
17.65 (0.24)
18.74 (0.25)
18.22 (0.25)
17.41 (0.24)
16.91 (0.23)
18.16 (0.25)
17.34 (0.24)
17.02 (0.24)
Table 3: Normal errors with 5% outliers mixed in, evaluated under the mixture distribution target
q
Method
QR
WQR0.1
WQR0.3
WQR0.5
QR.M
WQR.M0.1
WQR.M0.3
WQR.M0.5
WQR.M20.1
WQR.M20.3
WQR.M20.5
0.1
37.67 (0.64)
36.55 (0.61)
35.03 (0.58)
34.41 (0.57)
44.71 (0.82)
42.81 (0.77)
39.69 (0.69)
37.28 (0.65)
42.77 (0.77)
40.11 (0.71)
38.61 (0.69)
0.25
15.53 (0.20)
15.20 (0.19)
14.72 (0.19)
14.50 (0.19)
14.39 (0.18)
13.99 (0.17)
13.37 (0.17)
12.98 (0.16)
13.90 (0.17)
13.23 (0.17)
12.93 (0.17)
0.5
11.90 (0.15)
11.62 (0.14)
11.17 (0.14)
10.89 (0.14)
10.17 (0.12)
9.89 (0.12)
9.44 (0.11)
9.14 (0.11)
9.77 (0.12)
9.17 (0.11)
8.83 (0.11)
0.8
18.82 (0.25)
18.36 (0.25)
17.81 (0.24)
17.46 (0.24)
18.12 (0.24)
17.63 (0.23)
16.86 (0.22)
16.40 (0.22)
17.56 (0.23)
16.76 (0.23)
16.44 (0.23)
Table 4: Normal errors, but with 3% of cases having high leverage
q
Method
QR
WQR0.1
WQR0.3
WQR0.5
QR.M
WQR.M0.1
WQR.M0.3
WQR.M0.5
WQR.M20.1
WQR.M20.3
WQR.M20.5
0.1
27.13 (0.32)
27.22 (0.31)
27.76 (0.31)
28.70 (0.32)
22.98 (0.27)
23.01 (0.27)
23.25 (0.27)
23.84 (0.27)
23.04 (0.26)
23.65 (0.27)
24.94 (0.29)
0.25
17.15 (0.20)
17.22 (0.20)
17.36 (0.20)
17.74 (0.21)
13.62 (0.15)
13.61 (0.15)
13.76 (0.16)
14.14 (0.16)
13.62 (0.15)
13.91 (0.16)
14.56 (0.17)
2
0.5
14.46 (0.16)
14.37 (0.16)
14.42 (0.16)
14.62 (0.16)
11.02 (0.12)
10.94 (0.12)
10.95 (0.12)
11.14 (0.12)
10.87 (0.12)
10.85 (0.12)
11.10 (0.12)
0.8
18.97 (0.21)
19.05 (0.22)
19.42 (0.22)
19.88 (0.23)
15.41 (0.18)
15.40 (0.18)
15.55 (0.18)
15.97 (0.19)
15.41 (0.18)
15.73 (0.18)
16.52 (0.19)