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Biometrika 1983 70(1):67-88; doi:10.1093/biomet/70.1.67
© 1983 by Biometrika Trust
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Statistical analysis of empirical models fitted by optimization

D. A. JONES

Institutes of Hydrology Wallingford, Oxfordshire

Practical procedures for statistical inference about the parameters of empirical models are presented. These avoid the necessity of formulating an explicit statistical model and can allow for general statistical dependency within the data used for model fitting. The theory is an asymptotic one, and one which allows the construction of significance tests and confidence regions for subsets of the model parameters. Other results concern the comparison of structurally different models, and of different objective functions for parameter fitting.

Key Words: Asymptotic theory • Comparison of models • Empirical model • Numerical optimization • Objective function


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