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Non-linear regression in credibility theory. (English) Zbl 0579.62091

Author’s summary: Let X be a random vector with distribution depending on a parameter treated as a random variable \(\Theta\). The usual linear regression assumption is that E(X\(| \Theta)\) can be displayed in the form \(y\beta\) (\(\Theta)\) where y is a fixed design matrix and \(\beta\) (\(\Theta)\) an unknown vector.
In the present paper we assume that E(X\(| \Theta)\) is a rather arbitrary function f(\(\beta\) (\(\Theta)\)) of the unknown vector \(\beta\) (\(\Theta)\) and we derive credibility approximations for \(\beta\) (\(\Theta)\).
Reviewer: A.Reich

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62J02 General nonlinear regression
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References:

[1] De Vylder, F., Practical models in credibility theory, including parameter estimation, (De Vylder, F., Premium Calculation in Insurance. Premium Calculation in Insurance, NATO ASI Series. Series C: Math. and Phys. Sciences, Vol. 121 (1983)), Reidel · Zbl 0535.62081
[2] Hachemeister, C. A., (Kahn, P. M., Credibility for regression models with application to trend. Credibility for regression models with application to trend, Credibility, Theory and applications (1975), Academic Press: Academic Press New York) · Zbl 0354.62057
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