Hamilton, David C. A comparison of two exact confidence regions for partially nonlinear regression models. (English) Zbl 0624.62062 Can. J. Stat. 15, 127-135 (1987). Exact confidence regions for all the parameters in nonlinear regression models can be obtained by comparing the lengths of projections of the error vector into orthogonal subspaces of the sample space. In certain partially nonlinear models an alternative exact region is obtained by replacing the linear parameters by their conditional estimates in the projection matrices. An ellipsoidal approximation to the alternative region is obtained in terms of the tangent-plane coordinates, similar to one previously obtained for the more usual region. This ellipsoid can be converted to an approximate region for the original parameters and can be used to compare the two types of exact confidence regions. MSC: 62J02 General nonlinear regression 62F25 Parametric tolerance and confidence regions Keywords:efficient scores; partially nonlinear models; second-order approximation; Exact confidence regions; projections; orthogonal subspaces of the sample space; ellipsoidal approximation; tangent-plane coordinates PDFBibTeX XMLCite \textit{D. C. Hamilton}, Can. J. Stat. 15, 127--135 (1987; Zbl 0624.62062) Full Text: DOI References: [1] Bates, Relative curvature measures of nonlinearity (with discussion), J. Roy. Statist. Soc. Ser. B 42 pp 1– (1980) · Zbl 0455.62028 [2] Bates, Parameter transformations for improved approximate confidence regions in nonlinear least squares, Ann. Statist. 9 pp 1152– (1981) · Zbl 0493.62060 [3] Beale, Confidence regions in nonlinear estimation (with discussion), J. Roy. Statist. Soc. Ser. B 22 pp 41– (1960) · Zbl 0096.13201 [4] Cox, Theoretical Statistics (1974) · doi:10.1007/978-1-4899-2887-0 [5] Draper, Applied Regression Analysis (1981) · Zbl 0548.62046 [6] El-Shaarawi, Interval estimation in nonlinear models, Sankhyã Ser. B 42 pp 229– (1980) [7] Halperin, Confidence interval estimation in nonlinear regression, J. Roy. Statist. Soc. Ser. B 25 pp 330– (1963) · Zbl 0122.14303 [8] Hamilton, Confidence regions for parameter subsets in nonlinear regression, Biometrika 73 pp 57– (1986) · Zbl 0587.62133 [9] Hamilton, Accounting for intrinsic nonlinearity in nonlinear regression parameter inference regions, Ann. Statist. 10 pp 386– (1982) · Zbl 0537.62045 [10] Hartley, Exact confidence regions for the parameters in nonlinear regression laws, Biometrika 51 pp 347– (1964) · Zbl 0125.08703 · doi:10.1093/biomet/51.3-4.347 [11] Johansen, Some topics in regression, Scand. J. Statist. 10 pp 161– (1983) · Zbl 0541.62047 [12] Khuri, A note on D-optimal designs for partially nonlinear regression models, Technometrics 26 pp 59– (1984) · Zbl 0531.62067 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.