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

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  • Yatracos, Yannis G.

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.

Suggested Citation

  • Yatracos, Yannis G., 1989. "On the estimation of the derivatives of a function with the derivatives of an estimate," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 172-175, January.
    • Handle: RePEc:eee:jmvana:v:28:y:1989:i:1:p:172-175
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    Cited by:

    1. Luo, Xiaopeng & Lu, Zhenzhou & Xu, Xin, 2014. "Non-parametric kernel estimation for the ANOVA decomposition and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 140-148.
    2. George Roussas & Yannis Yatracos, 1996. "Minimum distance regression-type estimates with rates under weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 267-281, June.

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