Estimating covariance in a growth curve model
For a multivariate elliptically contoured random matrix Y with mean μ ∈ S 1 □ S 2 and covariance A ⊗ ∑, an explicit formula for the best quadratic unbiased estimator, \ ̂ bE(γ), of ∑ is obtained, where S i = { Z i b i : R′ i b i = M′ i u i for some u i } and S 1 □ S 2 is the linear span of the set o...
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| Published in | Linear algebra and its applications Vol. 214; pp. 103 - 118 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
1995
|
| Online Access | Get full text |
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| Summary: | For a multivariate elliptically contoured random matrix
Y with mean
μ ∈
S
1 □
S
2 and covariance
A ⊗ ∑, an explicit formula for the best quadratic unbiased estimator,
\
̂
bE(γ), of ∑ is obtained, where
S
i
= {
Z
i
b
i
:
R′
i
b
i
=
M′
i
u
i
for some
u
i
} and
S
1 □
S
2 is the linear span of the set of all
xy′ with
x ∈
S
1 and
y ∈
S
2. The distribution and the image set of
\
̂
bE(γ) are also obtained. None of the matrices
A, ∑,
Z
i
,
R
i
, and
M
i
are assumed to have full column rank. |
|---|---|
| ISSN: | 0024-3795 1873-1856 |
| DOI: | 10.1016/0024-3795(93)00057-7 |