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.
@article{104489, author = {Rastislav Potock\'y and Van Ban To}, title = {Confidence regions in nonlinear regression models}, journal = {Applications of Mathematics}, volume = {37}, year = {1992}, pages = {29-39}, zbl = {0749.62043}, mrnumber = {1152155}, language = {en}, url = {http://dml.mathdoc.fr/item/104489} }
Potocký, Rastislav; To, Van Ban. Confidence regions in nonlinear regression models. Applications of Mathematics, Tome 37 (1992) pp. 29-39. http://gdmltest.u-ga.fr/item/104489/
Relative curvature measures of nonlinearity, Journal of the Royal Statistical Society, Ser. B 42 (1980), 1-25. (1980) | MR 0567196
Parameter transformations for improved approximate confidence regions in nonlinear least squares, The Annals of Statistics 9 (1981), 1152-1167. (1981) | Article | MR 0630099
Application of digital computers in the exploration of functional relationships, Proc. I.E.E. 103 no. 1, part B, suppl. (1956), 100-107. (1956) | MR 0094906
Marginal curvatures and their usefulness in the analysis of nonlinear regression models, Journal of the American Statistical Association 82 (1987), 844-850. (1987) | Article | MR 0909991 | Zbl 0623.62062
Curvatures for parameter subsets in nonlinear regression, The Annals of Statistics 14 (1986), 1399-1418. (1986) | Article | MR 0868308
A note on parameter-effects curvature, Journal of the American Statistical Association 80 (1985), 872-878. (1985) | Article | MR 0819586
Nonlinear regression, The American Statistician 29 (1975), 73-81. (1975) | MR 0373177 | Zbl 0328.62043
Accounting for intrinsic nonlinearity in nonlinear regression parameter inference regions, The Annals of Statistics 10(1982), 386-393. (1982) | MR 0653514