Journal of Probability and Statistics / 2011 / Article / Tab 1 / Research Article
Determinant Efficiencies in Ill-Conditioned Models Table 1 Roots
𝐺
(
𝜷
)
and
𝜷
𝐺
(
𝑖
)
of generalized variances for
𝜷
and subset estimators
{
𝜷
𝑖
∈
ℝ
𝑡
}
, and angles
𝜙
(
1
𝑛
∶
𝐗
)
𝑑
𝑒
𝑔
between regressors and the constant, against reference values
𝜙
∗
∗
<
1
8
.
4
4
and
𝜙
∗
<
3
0
.
0
0
, in eight small second-order designs.
Design
𝐺
(
𝜷
)
̂
𝛽
𝐺
(
0
)
𝜷
𝐺
(
𝐿
)
𝜷
𝐺
(
𝑄
)
𝜷
𝐺
(
𝐼
)
𝜷
𝐺
(
𝑄
,
𝜷
𝐼
)
𝜷
𝐺
(
𝑀
)
𝜙
(
𝟏
𝑛
∶
𝐗
)
H
3
1
0
1.49916 5.0477 1.18821 2.08026 1.61045 1.83034 1.58484 25.11*
H
3
1
1
B
1.28050 10.0000 1.0000 1.17680 1.99997 1.53413 1.33017 17.55**
S
C
D
1.53876 10.0000 1.66667 1.04210 4.16667 2.08376 1.63142 17.55**
B
B
D
1.10533 10.0000 0.83333 1.64583 1.11111 1.35229 1.15077 16.10**
C
C
D
0.93725 10.0000 0.71429 1.03300 1.25000 1.13633 0.97341 14.96**
N
D
2.03063 8.7500 1.25000 7.80031 1.25000 3.12256 2.22030 18.80*
H
D
2.33258 5.0000 1.91189 6.61313 1.95275 3.57444 2.59004 25.24*
B
D
D
2.21835 4.6477 1.58809 4.96625 2.25752 3.22673 2.44950 26.25*
