Convolution power kernels for density estimation |
| |
Authors: | F Comte V Genon-Catalot |
| |
Institution: | Université Paris Descartes, Sorbonne Paris Cité, MAP5 UMR 8145, 45 rue des Saints Pères, 75270 Paris cedex 06, France |
| |
Abstract: | 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. |
| |
Keywords: | Adaptive estimators Density estimation Infinitely divisible distributions Kernel estimators Lower bounded support |
本文献已被 ScienceDirect 等数据库收录! |
|