| Title:
|
Estimation of dispersion in nonlinear regression models with constraints (English) |
| Author:
|
Kubáček, Lubomír |
| Author:
|
Tesaříková, Eva |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
75-86 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature. (English) |
| Keyword:
|
nonlinear regression model |
| Keyword:
|
linearization |
| Keyword:
|
estimation of dispersion |
| MSC:
|
62F10 |
| MSC:
|
62H12 |
| MSC:
|
62J02 |
| MSC:
|
62J05 |
| MSC:
|
65C60 |
| idZBL:
|
Zbl 1060.62067 |
| idMR:
|
MR2124605 |
| . |
| Date available:
|
2009-08-21T12:54:22Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132937 |
| . |
| Reference:
|
[1] Bates D. M., Watts D. G.: Relative curvatures measures of nonlinearity.J. Roy. Statist. Soc. B 42 (1980), 1–25. MR 0567196 |
| Reference:
|
[2] Kubáček L., Kubáčková L.: Regression models with a weak nonlinearity.Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67. |
| Reference:
|
[3] Kubáček L., Kubáčková L.: Statistics, Metrology. : Vyd. Univ. Palackého, Olomouc., 2000 (in Czech). |
| Reference:
|
[4] Kubáček L., Tesaříková E.: Confidence regions in nonlinear models with constraints.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 42 (2003), 43–58. Zbl 1046.62065, MR 2056021 |
| Reference:
|
[5] Rao C. R., Mitra S. K.: Generalized Inverse of Matrices, its Applications. : J. Wiley & Sons, New York–London–Sydney–Toronto., 1971. MR 0338013 |
| Reference:
|
[6] Scheffé H.: The Analysis of Variance. : J. Wiley, New York., 1959. MR 0116429 |
| Reference:
|
[7] Tesaříková E., Kubáček L.: Estimators of dispersion in models with constraints (demoprogram).Department of Algebra and Geometry, Faculty of Science, Palacký University, Olomouc, 2003. |
| . |
