I have a graph of some (highly nonlinear) experimental spectrum which is obtained by smoothing results of several repeated measurements obtained by different experimental methods. The graph also contains confidence bands obtained on the base of the spread of the original experimental values. I have no exact information on the number of observations and the graph is given as a continuous curve, so I must sample some points from it in order to use them in a fitting procedure. I have several nonlinear models which I wish to test on these data and estimate the confidence intervals for the parameters of the optimal model. The problem is that I do not know the number of actual degrees of freedom, so I cannot directly compare the models on the base of the F-test. I have tried to calculate the residual effective degrees of freedom for the sampled dataset but it just coincides with the number of points minus the number of independent variables.
What is the correct approach for selecting the optimal model when only smoothed continuous data is available?