Uniform error bounds for smoothing splines
نویسنده
چکیده
Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regression estimator itself, uniformly in the smoothing parameter over a wide range. This admits data-driven choices of the smoothing parameter.
منابع مشابه
Uniform Error Bounds for Smoothing Splines
Almost sure bounds are established for the uniform error of smoothing splines in nonparametric regression with random designs. Some kernel-like properties of the Green’s function for an appropriate boundary value problem are needed to reduce the problem to that for kernel-like regression estimators. Then, results of Einmahl and Mason (2005) imply the required bounds, uniformly in the smoothing ...
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