Joint behaviour of semirecursive kernel estimators of the location and of the size of the mode of a probability density function

Abdelkader Mokkadem (1) , Mariane Pelletier (1) , Baba Thiam (1)

1 LMV - Laboratoire de Mathématiques de Versailles

Let $\theta$ and $\mu$ denote the location and the size of the mode of a probability density. We study the joint convergence rates of semirecursive kernel estimators of $\theta$ and $\mu$. We show how the estimation of the size of the mode allows to measure the relevance of the estimation of its location. We also enlighten that, beyond their computational advantage on nonrecursive estimators, the semirecursive estimators are preferable to use for the construction on confidence regions.

Mots clés: Location and size of the mode; semirecursive estimation; central limit theorem; law of the iterated logarithm

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam. Joint behaviour of semirecursive kernel estimators of the location and of the size of the mode of a probability density function. Journal of Probability and Statistics, 2011, pp.ID 564297. ⟨10.1155/2011/564297⟩. ⟨hal-00201748⟩