Asymptotic Properties of Smoothing Parameter Selection in Spline Smoothing
نویسنده
چکیده
The asymptotic properties of smoothing parameter estimates for smoothing splines are developed. We consider a variety of estimates including Generalized Cross Validation, Generalized Maximum Likelihood, and more generally Type II ML estimates and the properties of the marginal posterior mode. Under the usual Sobolov space frequentist assumptions on the function to be estimated , consistency and asymptotic normality of the estimated smoothing parameter are proved. Our results show that the asymptotic distribution of the marginal posterior mode of the smoothing parameter does not depend on the prior distributions for a general class priors. The relative rates of convergence of the smoothing parameter estimates agree with those previously obtained for cross-validated kernel density estimates.
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