Asymptotics for $M$-Type Smoothing Splines
The Annals of Statistics · 1983 · Volume 11 · Issue 2
Abstract
Limit theorems giving rates of convergence of nonparametric regression estimates obtained from smoothing splines are proved. The main emphasis is on nonlinear, robust smoothing splines, but new results are obtained for the usual (linear) case. It is assumed that the knots become asymptotically uniform in a vague sense. Convergence of derivatives is also investigated. The main mathematical tools are a linearization of the robust smoothing spline, and an approximation of the linear smoothing spline utilizing the Green's function of an associated boundary value problem.
Keywords
41A15, 62F35, 62G05, 62J99, Nonparametric regression, robust estimation, smoothing splines
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