Section: New Results

Comparison of Kernel Density Estimators on Environmental Data with Assumption on Number of Modes

Participants : Jérôme Saracco, Raphaël Coudret.

In this work, we consider valvometric data samples, that is measurements of distances between the two parts of the shell of bivalves. The movements of a few oysters are monitored in different places (like Arcachon Bay or Santander port) by a laboratory called Environnements et Paléoenvironnements Océaniques et Continentaux (EPOC). The aim of these experiments is to determine water quality via the observation of the bivalves behavior. Previous related works have been published on this subject. EPOC team studied this animals in a copper pollution context via investigations using kernels methods. In our study, we consider each day the density of the distance between the two parts of the shell. This density is reasonably assumed to have 2 modes, the first one corresponds to a close status of the shell and the second one to an open status. The study of the evolution of this density along the time provides informations on bivalves behavior. We provide theoretical results on our bandwidth choice with a bounded support kernel and we give a procedure to determine this bandwidth. We also provide asymptotic results for a density kernel estimator with a kernel that has it support on $\Re$. We present an extensive simulation study in order to compare numerical performances of various density estimators based or not on the two modes assumption. From the results obtained from the simulated data, we derive the suitable estimator for our real data application. This work will be submitted for publication very soon and it has been presented in the international conference [37] .