Criteria for model evaluation in the case of deconvolution calculations

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Abstract
The time-resolved fluorescence relaxation obtained by a pulse method can be described by a convolution product of the measured excitation profile and the fluorescence response of the sample. In this paper, the behavior of this convolution model, with respect to the parameters, is examined. The model happens to be nearly linear in the neighborhood of the least-squares estimates, according to an adapted nonlinearity measure. As a consequence, the lack of fit-test and the extra sum of squares-test from the theory of linear models can be applied to decide how many components should be included in the fluorescence response function. The proposed method can be easily extended to other areas involving exponential relaxation.

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