Convolution power kernels for density estimation

Fabienne Comte (1) , Valentine Genon-Catalot (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We propose a new type of non-parametric density estimators fitted to random variables with lower or upper-bounded support. To illustrate the method, we focus on nonnegative random variables. The estimators are constructed using kernels which are densities of empirical means of m i.i.d. nonnegative random variables with expectation 1. The exponent m plays the role of the bandwidth. We study the pointwise mean square error and propose a pointwise adaptive estimator. The risk of the adaptive estimator satisfies an almost oracle inequality. A noteworthy result is that the adaptive rate is in correspondence with the smoothness properties of the unknown density as a function on (0,+∞). The adaptive estimators are illustrated on simulated data. We compare our approach with the classical kernel estimators.

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

Fabienne Comte, Valentine Genon-Catalot. Convolution power kernels for density estimation. Journal of Statistical Planning and Inference, 2012, 142 (7), pp.1698-1715. ⟨hal-00681309⟩