Abstract
The general nonlinear regression model is considered, where the error distribution can be nonnormal. In this paper we present tests, confidence intervals and estimators for both the regression coefficients and the variance of the observations which perform well in the sense of second order asymptotic theory. In particular, robustness results for deviations from the normal distribution are given including distributions with either known or unknown skewness and kurtosis.
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References
Pfanzagl, J. Asymptotic expansions related to minimum contrast estimators. Ann. of Statist. 1 (1973), 993–1026.
Pfanzagl, J. Asymptotically optimum estimation and test procedures. Proc. Prague Conf. on Asymptotic Methods of Statistics 1 (1973), 201–272.
Schmidt, W. H., Zwanzig, S. Second order asymptotics in nonlinear regression. Preprint 04/83, Akademie der Wissenschaften der DDR, Institut für Mathematik (1983).
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© 1984 Academy of Agricultural Sciences of the GDR, Research Centre of Animal Production, Dummerstorf-Rostock, DDR 2551 Dummerstorf.
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Schmidt, W.H., Zwanzig, S. (1984). Testing Hypotheses in Nonlinear Regression for Nonnormal Distributions. In: Rasch, D., Tiku, M.L. (eds) Robustness of Statistical Methods and Nonparametric Statistics. Theory and Decision Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6528-7_30
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DOI: https://doi.org/10.1007/978-94-009-6528-7_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6530-0
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