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Cardinal splines in nonparametric regression. (English) Zbl 1282.62097
Summary: We discuss a nonparametric regression model on an equidistant grid of the real line. A class of kernel type estimates based on the so-called fundamental cardinal splines will be introduced. Asymptotic optimality of these estimates will be established for certain functional classes. This model explains the often mentioned heuristic fact that cubic splines are adequate for most practical applications.

MSC:
62G08 Nonparametric regression and quantile regression
65D07 Numerical computation using splines
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