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A nonparametric statistical procedure for the detection of marine pollution |
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| Authors: | Bernard Bercu Sami Capderou Gilles Durrieu |
| Affiliation: | 1. Institut de Mathématiques de Bordeaux, Université de Bordeaux, Talence, France;2. Laboratoire de Mathématiques de Bretagne Atlantique, Université de Bretagne Sud, Vannes, France;3. Institut de Sciences Exactes et Appliquées, Université de la Nouvelle-Calédonie, Nouméa, Nouvelle-Calédonie, France |
| 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. |
| Keywords: | Environmental statistics and data analysis mathematical statistics nonparametric estimation fixed-design regression |