# Partial spline. Reference [closed]

I have a well done and perfectly working protocol to smooth my experimental data. I do the following:

I have a variable of size 1000. Iteratively I choose random 100 points and spline them using the cubic algorithm. After this I have a number of splines, the result of this 'smoothing' is an average spline. The problem is that it is absolutely self-made protocol.

Could you help me with a reference for a such approach?

Your described methodology appears as an implementation of bagging; it is usually seen as a variance reduction technique. Bagging commonly utilises regression or classification trees as base-learners but using a cubic spline is also perfectly fine; the Wikipedia link shows a use-case where the base learner in LOESS smoother. In short, when implementing bagging we combine $$B$$ approximating functions (learners) $$f_b(X)$$, $$b = 1, \dots, B$$ which are train on $$B$$ bootstrap samples of the training data set. Our final bagging predictor is then the average $$f(X)_{bagging} = \frac{1}{B} \sum_1^B f_b(X)$$.