| Title:
|
Admissible invariant estimators in a linear model (English) |
| Author:
|
Stępniak, Czesław |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
310-321 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbf{y}$ be observation vector in the usual linear model with expectation $\mathbf{A\beta }$ and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic $\mathbf{a}^{T} \mathbf{y}$ is called invariant estimator for a parametric function $\phi = \mathbf{c}^{T}\mathbf{\beta }$ if its MSE depends on $\mathbf{\beta }$ only through $\phi $. It is shown that $ \mathbf{a}^{T}\mathbf{y}$ is admissible invariant for $\phi $, if and only if, it is a BLUE of $\phi ,$ in the case when $\phi $ is estimable with zero variance, and it is of the form $k\widehat{\phi }$, where $k\in \left\langle 0,1\right\rangle $ and $ \widehat{\phi }$ is an arbitrary BLUE, otherwise. This result is used in the one- and two-way ANOVA models. Our paper is self-contained and accessible, also for non-specialists. (English) |
| Keyword:
|
linear estimator |
| Keyword:
|
invariant estimator |
| Keyword:
|
admissibility |
| Keyword:
|
one-way/two-way ANOVA |
| MSC:
|
62C05 |
| MSC:
|
62C15 |
| MSC:
|
62J05 |
| MSC:
|
62J10 |
| idZBL:
|
Zbl 1297.62157 |
| idMR:
|
MR3245533 |
| DOI:
|
10.14736/kyb-2014-3-0310 |
| . |
| Date available:
|
2014-07-29T13:04:44Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143878 |
| . |
| Reference:
|
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