Model Order Selection for Savitzky–Golay Smoothers via N-fold Cross-Validation

Savitzky-Golay (SG) smoothers are noise suppressing filters operating on the principle of projecting noisy input to the subspace of polynomials. A poorly selected polynomial order results in over-/under-smoothing which shows as either bias or excessive noise at the output. In this study, we apply N-fold cross-validation technique, also called leave-one-out cross-validation, for the model order selection and show that the inherent analytical structure of the SG filtering problem, mainly its minimum norm formulation, enables an efficient and effective order selection solution. The suggested solution compares favorably with the state of art Bayesian Information Criterion (BIC) rule in the non-asymptotic signal-to-noise ratio (SNR) and sample size regimes. MATLAB codes for the method and numerical experiments are provided to reproduce the given results. This capsule reproduces the numerical experiments given in the article.