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A comparison of a spline estimate to its equivalent kernel estimate. (English) Zbl 0741.62040
Summary: It has been observed that to a smoothing spline operator there corresponds an equivalent kernel operator; these two operators have been compared in a variety of norms. We refine the existing bounds for the particular case of the spline estimator considered by J. Rice and M. Rosenblatt [ibid. 11, 141-156 (1983; Zbl 0535.41019)] and its corresponding equivalent kernel estimator.
We obtain detailed asymptotic expressions for the bias and covariance functions of the two estimates and provide rates of convergence. Direct comparison then shows that the two estimates are similar. They may differ somewhat in their higher order boundary behavior.

MSC:
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62J02 General nonlinear regression
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