Variance Reduction in Smoothing Splines

We develop a variance reduction method for smoothing splines. We do this by showing that the quadratic interpolation method introduced in Cheng et al. (2006), for local linear estimators, also works for smoothing splines. For a given point of estimation, Cheng et al. (2006) define a variance-reduced local linear estimate as a linear combination of classical estimates at three nearby points. We use equivalent kernel function results from Nychka (1995) and Lin et al. (2004) in the development of our methodologies. First, we develop a variance reduction method for spline estimators in univariate regression models. Next, we develop an analogous variance reduction method for spline estimators in clustered/longitudinal models. Finally, simulation studies are performed which demonstrate the efficacy of our variance reduction methods in finite sample settings.