On the estimation of the derivatives of a function with the derivatives of an estimate

Yannis G. Yatracos

Journal of Multivariate Analysis, 1989, vol. 28, issue 1, 172-175

Abstract: 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.

Keywords: estimation; of; the; derivatives; of; a; function; rates; of; convergence; bounds; on; the; norm; difference; of; the; derivatives; of; smooth; functions (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (2)

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