# Smoothing noisy data with spline functions

@article{Craven1978SmoothingND, title={Smoothing noisy data with spline functions}, author={Peter Craven and Grace Wahba}, journal={Numerische Mathematik}, year={1978}, volume={31}, pages={377-403} }

SummarySmoothing splines are well known to provide nice curves which smooth discrete, noisy data. We obtain a practical, effective method for estimating the optimum amount of smoothing from the data. Derivatives can be estimated from the data by differentiating the resulting (nearly) optimally smoothed spline.We consider the modelyi(ti)+εi,i=1, 2, ...,n,ti∈[0, 1], whereg∈W2(m)={f:f,f′, ...,f(m−1) abs. cont.,f(m)∈ℒ2[0,1]}, and the {εi} are random errors withEεi=0,Eεiεj=σ2δij. The error variance…

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