| Title:
|
Locally and uniformly best estimators in replicated regression model (English) |
| Author:
|
Volaufová, Júlia |
| Author:
|
Kubáček, Lubomír |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
5 |
| Year:
|
1983 |
| Pages:
|
386-390 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of the paper is to estimate a function $\gamma=tr(D\beta\beta')+tr(C\sum)$ (with $d, C$ known matrices) in a regression model $(Y, X\beta,\sum)$ with an unknown parameter $\beta$ and covariance matrix $\sum$. Stochastically independent replications $Y_1,\ldots, Y_m$ of the stochastic vector $Y$ are considered, where the estimators of $X\beta$ and $\sum$ are $\bar{Y}=\frac 1 m \sum ^m _{i=1} Y_i$ and $\hat{\sum}=(m-1)^{-1} \sum^m_{i=1}(Y_i-\bar{Y})(Y_i-\bar{Y})'$, respectively. Locally and uniformly best inbiased estimators of the function $\gamma$, based on $\bar{Y}$ and $\hat{\sum}$, are given. (English) |
| Keyword:
|
replicated regression model |
| Keyword:
|
best unbiased estimators |
| MSC:
|
62H12 |
| MSC:
|
62J05 |
| idZBL:
|
Zbl 0529.62056 |
| idMR:
|
MR0712914 |
| DOI:
|
10.21136/AM.1983.104049 |
| . |
| Date available:
|
2008-05-20T18:23:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104049 |
| . |
| Reference:
|
[1] Jürgen Kleffe: C. R. Rao's MINQUE for replicated and multivariate observations.Lecture Notes in Statistics 2. Mathematical Statistics and Probability Theory. Proceedings Sixth International Conference. Wisla (Poland) 1978. Springer N. York, Heidelberg, Berlin 1979, 188-200. |
| Reference:
|
[2] Jürgen Kleffe, Júlia Volaufová: Optimality of the sample variance-covariance matrix in repeated measurement designs.(Submitted to Sankhyā). |
| Reference:
|
[3] C. R. Rao: Linear Statistical Inference and Its Applications.J. Wiley, N. York 1965. Zbl 0137.36203, MR 0221616 |
| Reference:
|
[4] C. R. Rao S. K. Mitra: Generalized Inverse of Matrices and Its Applications.J. Wiley, N. York 1971. MR 0338013 |
| Reference:
|
[5] R. Thrum J. Kleffe: Inequalities for moments of quadratic forms with applications to a.s. convergence.Math. Operationsforsch. Statistics Ser. Statistics (in print). MR 0704788 |
| . |
