Davies, Robert; Withers, Christopher; Nadarajah, Saralees Confidence intervals in a regression with both linear and non-linear terms. (English) Zbl 1274.62213 Electron. J. Stat. 5, 603-618 (2011). Summary: We present a simple way for calculating confidence intervals for a class of scalar functions of the parameters in least squares estimation when there are linear together with a small number of non-linear terms. We do not assume normality. MSC: 62F25 Parametric tolerance and confidence regions Keywords:confidence interval; estimation; optimization; two-phase regression × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Bates, D. M. and Watts, D. G. (1988)., Nonlinear Regression Analysis and Its Applications . John Wiley and Sons, New York. · Zbl 0728.62062 [2] Beek, P. J., Schmidt, R. C., Morris, A. W., Sim, M. Y. and Turvey, M. T. (1995). Linear and nonlinear stiffness and friction in biological rhythmic movements., Biological Cybernetics 73 499-507. · Zbl 1066.92501 · doi:10.1007/BF00199542 [3] Carroll, R. J. and Ruppert, D. (1988)., Transformation and Weighting in Regression . Chapman and Hall, New York. · Zbl 0666.62062 [4] Carroll, R. J., Ruppert, D., Stefanski, L. A. and Crainiceanu, C. M. (2006)., Measurement Error in Nonlinear Models: A Modern Perspective , second edition. Chapman and Hall/CRC, Boca Raton, Florida. · Zbl 1119.62063 [5] Casella, G. and Berger, R. L. (2002)., Statistical Inference , second edition. Duxbury Press, Belmont, California. · Zbl 0699.62001 [6] Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative., Biometrika 74 33-43. · Zbl 0612.62023 [7] Donaldson, J. R. and Schnabel, R. B. (1987). Computational experience with confidence regions and confidence intervals for nonlinear least squares., Technometrics 29 67-82. · Zbl 0611.62034 · doi:10.2307/1269884 [8] Hawkins, D. M. (1980). A note on continuous and discontinuous segmented regressions., Technometrics 22 443-444. · Zbl 0455.62053 · doi:10.2307/1268331 [9] Honore, B. E. (1992). Trimmed LAD and least squares estimation of truncated and censored regression models with fixed effects., Econometrica 60 533-565. · Zbl 0760.62070 · doi:10.2307/2951583 [10] Hu, F. and Kalbfleisch, J. D. (2000). The estimating function bootstrap., Canadian Journal of Statistics 28 449-499. · Zbl 0977.62045 · doi:10.2307/3315958 [11] Huet, S., Bouvier, A., Poursat, M. -A. and Jolivet, E. (2004)., Statistical Tools for Nonlinear Regression: A Practical Guide with S-PLUS and R Examples , second edition. Springer Verlag, New York. · Zbl 1041.62053 [12] Kaniovskaya, I. Yu. (1980). On the asymptotic distribution of the Robbinsmhy Monro procedure with a nonsmooth regression function., Theory of Probability and Mathematical Statistics 23 69-74. · Zbl 0474.62079 [13] Lindsey, J. K. (2001)., Nonlinear Models in Medical Statistics . Oxford University Press, Oxford. · Zbl 1063.62597 [14] Manski, C. F. (1988)., Analog Estimation Methods in Econometrics . Chapman and Hall, New York. · Zbl 0775.62337 [15] Seber, G. A. F. and Wild, C. J. (1989)., Nonlinear Regression . John Wiley and Sons, New York. · Zbl 0721.62062 [16] Shacham, M. and Brauner, N. (2000). A general framework for considering data precision in optimal regression models. In:, Proceedings of the Fifth International Conference on Foundations of Computer-Aided Process Design , editors M. F. Malone and J. A. Trainham, volume 96, pp. 470-473. [17] Siewicki, T. C., Pullaro, T., Pan, W., McDaniel, S., Glenn, R. and Stewart, J. (2007). Models of total and presumed wildlife sources of fecal coliform bacteria in coastal ponds., Journal of Environmental Management 82 120-132. [18] Tian, L., Liu, J. and Wei, L. J. (2007). Implementation of estimating function based inference procedure with MCMC samplers., Journal of the American Statistical Association 102 897-900. · doi:10.1198/016214507000000725 [19] Trentin, E., Magnoni, L. and Andronico, A. (2003). Toward a modular connectionist model of local chlorophyll concentration from satellite images. In:, Proceedings of the International Joint Conference on Neural Networks , volumes 1-4, pp. 2317-2321. 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.