Strong consistency of the mode of multivariate recursive kernel density estimator under strong mixing hypothesis

Fatma Ben Khadher^a, Yousri Slaoui<sup>b

a</sup> Univ. Monastir, Laboratoire analyse, geométrie et applications, FSM, Tunisie
^b Univ. Poitiers, Lab. Math. et Appl., Futuroscope Chasseneuil, France

Abstract: In this research paper, we define a kernel estimator of the mode based on the recursive kernel density estimator developed by [23]. In addition, we establish its almost sure convergence under strong mixing hypothesis. Finally, we corroborate these theoretical results through numerical simulations.

Keywords: Nonparametric estimation, Density estimation, Stochastic approximation, Mode, Strong mixing, Strong consistency.

MSC: 62G05; 62G07; 62L20; 62E20; 60F05; 60E05

Language: English