A1762
Title: Asymptotic theory for exponentially weighted aggregated penalized splines
Authors: Youngseok Song - West Virginia University (United States) [presenting]
Abstract: Theoretical properties of an exponentially weighted aggregated (EWA) penalized spline estimator are studied. Rather than selecting a single smoothing parameter for penalized splines, the EWA estimator aggregates spline estimates over a range of smoothing parameters using a data-driven, exponentially weighted pseudo-posterior distribution. Conditions on prior distributions are derived under which the estimator achieves the optimal convergence rate in terms of average mean squared error, as well as consistency and asymptotic normality. In particular, the EWA estimator is shown to be asymptotically equivalent to regression spline estimators through aggregation over smoothing parameters under such priors. Technical challenges are addressed by developing a novel analysis of eigenvalue problems associated with the B-spline basis, which differs from traditional random matrix theory. A simulation study illustrates the finite-sample performance of the proposed estimator, and a data application demonstrates its practical use.
