| Title:
|
Linearization regions for a confidence ellipsoid in singular nonlinear regression models (English) |
| Author:
|
Kubáček, Lubomír |
| Author:
|
Tesaříková, Eva |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
73-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A construction of confidence regions in nonlinear regression models is difficult mainly in the case that the dimension of an estimated vector parameter is large. A singularity is also a problem. Therefore some simple approximation of an exact confidence region is welcome. The aim of the paper is to give a small modification of a confidence ellipsoid constructed in a linearized model which is sufficient under some conditions for an approximation of the exact confidence region. (English) |
| Keyword:
|
Nonlinear regression model |
| Keyword:
|
confidence region |
| Keyword:
|
singularity |
| MSC:
|
62F10 |
| MSC:
|
62J05 |
| idZBL:
|
Zbl 1191.62119 |
| idMR:
|
MR2641949 |
| . |
| Date available:
|
2010-02-11T13:56:17Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137506 |
| . |
| Reference:
|
[1] Bates, D. M., Watts, D. G.: Relative curvature measures of nonlinearity.J. Roy. Stat. Soc. B 42 (1980), 1–25. Zbl 0455.62028, MR 0567196 |
| Reference:
|
[2] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models, Regularity and Singularities.Academia, Praha, 2007. |
| Reference:
|
[3] Kubáček, L., Kubáčková, L.: Regression models with a weak nonlinearity.Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67. |
| Reference:
|
[4] Kubáček, L., Kubáčková, L.: Statistics and Metrology.Vyd. Univ. Palackého, Olomouc, 2000 (in Czech). |
| Reference:
|
[5] Kubáček, L., Tesaříková, E.: Linearization region for confidence ellispoids.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 47 (2008), 101–113. MR 2482720 |
| Reference:
|
[6] Pázman, A.: Nonlinear Statistical Models.Kluwer Academic Publisher, Dordrecht–Boston–London and Ister Science Press, Bratislava, 1993. MR 1254661 |
| Reference:
|
[7] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications.J. Wiley, New York–London–Sydney–Toronto, 1971. Zbl 0236.15005, MR 0338013 |
| Reference:
|
[8] Scheffé, H.: The Analysis of Variance.J. Wiley, New York–London–Sydney, 1967 (fifth printing). MR 1673563 |
| . |
