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The effectiveness of non-parametric, kernel-based methods for functionestimation comes at the price of high computational complexity, which hinderstheir applicability in adaptive, model-based control. Motivated byapproximation techniques based on sparse spectrum Gaussian processes, we focuson models given by regularized trigonometric linear regression. This paperprovides an analysis of the performance of such an estimation set-up within thestatistical learning framework. In particular, we derive a novel bound for thesample error in finite-dimensional spaces, accounting for noise withpotentially unbounded support. Next, we study the approximation error anddiscuss the bias-variance trade-off as a function of the regularizationparameter by combining the two bounds.

Error analysis of regularized trigonometric linear regression with unbounded sampling: a statistical learning viewpoint