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On a projection estimator of the regression function derivative

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  • Fabienne Comte
  • Nicolas Marie

Abstract

In this paper, we study the estimation of the derivative of a regression function in a standard univariate regression model. The estimators are defined either by derivating nonparametric least-squares estimators of the regression function or by estimating the projection of the derivative. We prove two simple risk bounds allowing to compare our estimators. More elaborate bounds under a stability assumption are then provided. Bases and spaces on which we can illustrate our assumptions and first results are both of compact or noncompact type, and we discuss the rates reached by our estimators. They turn out to be optimal in the compact case. Lastly, we propose a model selection procedure and prove the associated risk bound. To consider bases with a noncompact support makes the problem difficult.

Suggested Citation

  • Fabienne Comte & Nicolas Marie, 2023. "On a projection estimator of the regression function derivative," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 35(4), pages 773-819, October.
    • Handle: RePEc:taf:gnstxx:v:35:y:2023:i:4:p:773-819
    DOI: 10.1080/10485252.2023.2209198
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