I carry out a polynomial function approximation to a load duration curve (monotone decreasing function). I can approximate the load duration curve by using polynomial degrees from 4 to 12. I need an objective criterion to select the degree of polynomial considering a tradeoff between accuracy and included number of parameters in the function. Statistically, one can use adjusted $R^2$ or information criterion. But these statistical criteria do not work because the residuals are nonlinear (not suitable for adjusted $R^2$) and also I use least squares (do not have maximum likelihood value). Is there any other criterion to choose the adequate degree of polynomial from $4$th to $12$th degree?
