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 R2 or information criterion. But these statistical criteria do not work because the residuals are nonlinear (not suitable for adjusted R2) 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 4th to 12th degree?