A Comparison of Generalized Cross Validation and Modified Maximum Likelihood for Estimating the Parameters of a Stochastic Process

Wahba compared the performance of generalized cross validation (GCV) and modified maximum likelihood (MML) procedures for choosing the smoothing parameter of a smoothing spline. This work makes a more careful study of the two procedures when the stochastic model motivating the modified maximum likelihood estimate is correct. It is shown that in the case of the linear smoothing spline with equally spaced observations, both estimates are asymptotically normal with the GCV estimate having twice the asymptotic variance of the MML estimate. The impact of using these estimates on the subsequent predictions is also calculated

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