ABSTRACT
This paper is devoted to the estimation of the derivative of the regression function in fixed-design nonparametric regression. We establish the almost sure convergence as well as the asymptotic normality of our estimate. We also provide concentration inequalities which are useful for small sample sizes. Numerical experiments on simulated data show that our nonparametric statistical procedure performs very well. We also illustrate our approach on high-frequency environmental data for the study of marine pollution.
Acknowledgments
The authors would like to thank the editor and the two anonymous reviewers for their helpful comments and constructive suggestions which helped to improve the paper substantially.
Disclosure statement
No potential conflict of interest was reported by the authors.