In this article, we consider an alternative estimator of the conditional mode when the explanatory variable takes values in a semimetric space. This alternative estimate is based in a recursive kernel method. Under the ergodicity hypothesis, we quantify the asymptotic properties of this estimate, by giving the almost complete convergence rate. The asymptotic normality of this estimate is also given. Our approach is illustrated by a real data application.
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A recursive kernel estimate of the functional modal regression under ergodic dependence condition
Fatima Zohra Ardjoun Laboratoire de Statistique et Processus Stochastiques, Université de Sidi Bel Abbès, Sidi Bel Abbès, Algeria, Larbi Ait Hennani Institut Universitaire de Technologie, Universitè de Lille, Roubaix, France & Ali Laksaci Laboratoire de Statistique et Processus Stochastiques, Université de Sidi Bel Abbès, Sidi Bel Abbès, AlgeriaCorrespondencealialk@yahoo.fr
Fatima Zohra Ardjoun Laboratoire de Statistique et Processus Stochastiques, Université de Sidi Bel Abbès, Sidi Bel Abbès, Algeria, Larbi Ait Hennani Institut Universitaire de Technologie, Universitè de Lille, Roubaix, France & Ali Laksaci Laboratoire de Statistique et Processus Stochastiques, Université de Sidi Bel Abbès, Sidi Bel Abbès, AlgeriaCorrespondencealialk@yahoo.fr
Pages 475-496
Received 17 Oct 2015
Accepted 24 Apr 2016
Accepted author version posted online: 29 Apr 2016
Published online: 29 Apr 2016
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