Uniform-in-Bandwidth Nearest-Neighbor Density Estimation

Sarah Ouadah (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

We present a new sharp uniform-in-bandwidth limit law for the nearest-neighbor density estimator. Our result is established in the framework of convergence in probability, and we allow the bandwidth to vary within the complete range for which the estimator is consistent. We provide the explicit value of the asymptotic limiting constant for the sup-norm of the estimator's random error.

Mots clés: Convergence in probability; Nonparametric density estimation; Nearest-neighbor estimator; Uniform quantile process; Functional limit laws; Convergence in probability.

Domaines: Théorie [stat.TH]

Sarah Ouadah. Uniform-in-Bandwidth Nearest-Neighbor Density Estimation. 2012. ⟨hal-00766606⟩