| Title:
|
Confidence regions in nonlinear regression models (English) |
| Author:
|
Potocký, Rastislav |
| Author:
|
To, Van Ban |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
29-39 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
New curvature measures for nonlinear regression models are developed and methods of their computing are given. Using these measures, more accurate confidence regions for parameters than those based on linear or quadratic approximations are obtained. (English) |
| Keyword:
|
nonlinear regression |
| Keyword:
|
confidence regions |
| Keyword:
|
weak intrinsic and weak parameter-effects curvatures |
| Keyword:
|
linear approximation |
| Keyword:
|
curvature measures |
| Keyword:
|
quadratic approximations |
| Keyword:
|
likelihood ratios |
| MSC:
|
62F25 |
| MSC:
|
62J02 |
| idZBL:
|
Zbl 0749.62043 |
| idMR:
|
MR1152155 |
| DOI:
|
10.21136/AM.1992.104489 |
| . |
| Date available:
|
2008-05-20T18:42:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104489 |
| . |
| Reference:
|
[1] D. M. Bates D. G. Watts: Relative curvature measures of nonlinearity.Journal of the Royal Statistical Society, Ser. B 42 (1980), 1-25. MR 0567196 |
| Reference:
|
[2] D. M. Bates D. G. Watts: Parameter transformations for improved approximate confidence regions in nonlinear least squares.The Annals of Statistics 9 (1981), 1152-1167. MR 0630099, 10.1214/aos/1176345633 |
| Reference:
|
[3] G. E. P. Box G. A. Coutie: Application of digital computers in the exploration of functional relationships.Proc. I.E.E. 103 no. 1, part B, suppl. (1956), 100-107. MR 0094906 |
| Reference:
|
[4] G. P. I. Clarke: Marginal curvatures and their usefulness in the analysis of nonlinear regression models.Journal of the American Statistical Association 82 (1987), 844-850. Zbl 0623.62062, MR 0909991, 10.1080/01621459.1987.10478507 |
| Reference:
|
[5] R. D. Cook M. L. Goldberg: Curvatures for parameter subsets in nonlinear regression.The Annals of Statistics 14 (1986), 1399-1418. MR 0868308, 10.1214/aos/1176350166 |
| Reference:
|
[6] R. D. Cook J. A. Witmer: A note on parameter-effects curvature.Journal of the American Statistical Association 80 (1985), 872-878. MR 0819586, 10.1080/01621459.1985.10478196 |
| Reference:
|
[7] A. R. Gallant: Nonlinear regression.The American Statistician 29 (1975), 73-81. Zbl 0328.62043, MR 0373177 |
| Reference:
|
[8] D. C. Hamilton D. G. Watts D. M. Bates: Accounting for intrinsic nonlinearity in nonlinear regression parameter inference regions.The Annals of Statistics 10(1982), 386-393. MR 0653514 |
| . |
