| Title:
|
Linear-quadratic estimators in a special structure of the linear model (English) |
| Author:
|
Wimmer, Gejza |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
81-105 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the linear model with uncorrelated observations. The dispersions of the values observed are linear-quadratic functions of the unknown parameters of the mean (measurements by devices of a given class of precision). Investigated are the locally best linear-quadratic unbiased estimators as improvements of locally best linear unbiased estimators in the case that the design matrix has none, one or two linearly dependent rows. (English) |
| Keyword:
|
parametric estimation |
| Keyword:
|
linear model with variances depending on the mean value parameters |
| Keyword:
|
locally best linear-quadratic unbiased estimator (LBLQUE) |
| MSC:
|
62F10 |
| MSC:
|
62F99 |
| MSC:
|
62H12 |
| MSC:
|
62J99 |
| idZBL:
|
Zbl 0832.62050 |
| idMR:
|
MR1314481 |
| DOI:
|
10.21136/AM.1995.134282 |
| . |
| Date available:
|
2009-09-22T17:46:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134282 |
| . |
| Reference:
|
[1] V. Fajt: Electrical measurements.SNTL/ALFA, Praha, 1978. (Czech) |
| Reference:
|
[2] Guido del Pino: The unifying role of iterative generalized least squares in statistical algorithms.Statistical Science 4 (1980), 394–408. MR 1041764 |
| Reference:
|
[3] J. Nelder and R. Wedderburn: Generalized linear models.J. Roy. Statist. Soc. Ser A (1972), 370–384. 10.2307/2344614 |
| Reference:
|
[4] C.R. Rao and S.K. Mitra: Generalized Inverse of Matrices and Its Applications.J. Willey, New York, 1971. MR 0338013 |
| Reference:
|
[5] K. Rinner and F. Benz: Jordan/Eggert/Kneissl Handbuch der Vermessungskunde.Band VI, Stuttgart, 1966. |
| Reference:
|
[6] R. Wedderburn: Quasi-likelihood functions, generalized linear models and the GaussNewton method.Biometrika 61 (1974), 439–447. MR 0375592 |
| Reference:
|
[7] G. Wimmer: Linear model with variance depending on the mean value.Mathematica Slovaca 42 (1992), 223–238. MR 1170107 |
| Reference:
|
[8] G. Wimmer: Estimation in a special structure of the linear model.Mathematica Slovaca 43 (1993), 221–264. Zbl 0779.62061, MR 1274604 |
| . |
