G. Ferrari-Trecate and G. De Nicolao. Computing the equivalent number of parameters of fixed-interval smoothers. Proc. 40th IEEE Conference on Decision and Control , 3:2905--2910, 2001. Orlando (FL), US.
The problem of reconstructing an unknown signal fromn noisy samples can be addressed by means of non-parametric estimation techniques such as Tikhonov reg-ularization, Bayesian regression and state-space fixed-interval smoothing. The practical use of these ap-proaches calls for the tuning of a regularization param-eter that controls the amount of smoothing they intro-duce. The leading tuning criteria, including GeneralizedCross Validation and Maximum Likelihood, involve therepeated computation of the so-called equivalent num-ber of parameters, a normalized measure of the ﬂexi-bility of the nonparametric estimator. The paper de-velops new state-space formulas for the computation ofthe equivalent number of parameters in O(n) operations.The results are specialized to the case of uniform sam-pling yielding closed-form expressions of the equivalentnumber of parameters for both linear splines and first-order deconvolution.