Abstract
We consider the regression model y i = α + β exp (γ xi) + ei (γ < 0) with i. i. d. error variables e i with E(ei) = 0, V(ei) = σ2. By simulation experiments we investigate the possibility of using the elements of the sequence VA(n) (n = 4,…) as approximations of the variance v(\(\hat \vartheta \)) of the least squares estimator \(\hat \vartheta \) of θ’ = (α, β, γ) = (θ1θ2θ3). Here VA (n) is equal to
We find that approximations for the estimation problem are already good for n = 4 and very good from n = 6 on. Tests and confidence intervals in respect of γ can easily be constructed with sufficient accuracy from n = 4 on. We also investigate the robustness of the proposed test against non-normality.
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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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Rasch, D., Schimke, E. (1984). A Test for Exponential Regression and its Robustness. 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_25
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DOI: https://doi.org/10.1007/978-94-009-6528-7_25
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