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On fitting exponential regressions

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Summary

In this paper we propose a method of fitting the exponential regression\(E(y) = \alpha _O + \sum\limits_{i = 1}^p {\alpha _i e^{ - \lambda } i^x } \) by the structural theory of inference due to Fraser (1968). Using this theory we obtain the marginal likelihood function for the parameters λ′=(λ1, …, λp). The estimates of α′=(αO,…, αp) are obtained by solving a linear system of equations depending on functions of λ1, λ2,…, λp.

The marginal likelihood function of the λ-parameters is studied and an iterative scheme is developed to solve the maximization problem on the marginal likelihood function with respect to λ-parameters. Two examples are given to illustrate the procedure. Some inference procedure is indicated based on the graphs of the likelihood ratio function.

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Authors and Affiliations

  1. Department of Mathematics, Carleton University, K1S 5B6, Ottawa, Kanada

    A. E. Saleh & G. H. Choudhry

Authors
  1. A. E. Saleh
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  2. G. H. Choudhry
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Saleh, A.E., Choudhry, G.H. On fitting exponential regressions. Statistische Hefte 16, 213–222 (1975). https://doi.org/10.1007/BF02923000

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  • DOI: https://doi.org/10.1007/BF02923000

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