Smoothing Parameter Selection for Smoothing Splines A Simulation Study.pdf

Smo othing Parameter Selection for Smo othing Splines A Simulation Study Thomas C M Leey June revised May Abstract Smo othing splines are a p opular metho d for p erforming nonparametric regression Most imp ortant in the implementation of this metho d is the choice of the smo othing parameter This article provides a simulation study of several smo othing parameter selection metho ds including two socalled risk estimation metho ds To the b est of the authors knowledge the empirical p erformances of these two risk estimation metho ds have never b een rep orted in the literature Empirical conclusions from and recommen dations based on the simulation results will b e provided One noteworthy empirical observation is that the p opular metho d generalized crossvalidation was outp erformed by another metho d an improved Akaike Information criterion that shares the same assumptions and computational complexity Keywords exact double smo othing nonparametric regression plugin metho ds risk estimation roughness p enalty smo othing parameter smo othing splines Running Title Smo othing Spline Smo othing Parameter Selection y Postal Department of Statistics Colorado State University Fort Collins CO USA Email tleestatcolostateedu Phone Fax Intro duction This article studies the problem of nonparametric regression using smo othing splines Sup p ose observed are n pairs of measurements x y i n relating to the mo del i i y f x a x x b iid N 2 i i i 1 n i