On the estimation of the derivatives of a function with the derivatives of an estimate
Let [theta]n(x) be an estimator of a smooth function [theta](x). It is proved that [theta](x) can be estimated easier than its derivative [theta](s)(x), providing for [theta]n(s) - [theta](s)q an upper bound that depends on [theta]n - [theta]q. The same bound can be used as a tool to derive automatically rates of convergence when we are estimating derivatives of densities or regression functions.
Year of publication: |
1989
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Authors: | Yatracos, Yannis G. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 28.1989, 1, p. 172-175
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Publisher: |
Elsevier |
Keywords: | estimation of the derivatives of a function rates of convergence bounds on the norm difference of the derivatives of smooth functions |
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