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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?

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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 $f(X)_{bagging} = \frac{1}{B} \sum_1^B f_b(X)$.

Two standard paper references are: 1. Breiman (1996) Bagging predictors and 2. Bühlmann & Yu (2002) Analyzing bagging. If you prefer books, Berk's book Statistical Learning from a Regression Perspective has a short but very clear and insightful chapter (Chapt. 4) on bagging too.

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