I have datasets that can form several different curvy patterns between the dependent and independent variables. The 'true' relationship likely depends on a large number of factors that aren't easily measured and so it remains unknown. One method of describing this relationship has been through LOESS.
However, I am trying to optimize the LOESS fit by changing the tuning parameter (span or f-value) using k-fold cross-validation (with the loess.wrapper function in the bisoreg package in R). I mostly understand how the optimal span is chosen by minimizing the estimated predictive error via the CV. I've been studying the bias-variance tradeoff topic in sources such as Elements of Statistical Learning and I'm still left with a difficult question. Is it possible to calculate (or estimate) the bias and variance of a LOESS fit for different span values? I'd like to be able to compare different LOESS fits on the same data with these statistics but I think the issue lies in the fact that I don't know the 'true' relationship of the data.
Any guidance or recommended readings are appreciated.