Convolution power kernels for density estimation
- 作者：F. Comte ; fabienne.comte@parisdescartes.fr ; V. Genon-Catalot
- 关键词：Adaptive estimators ; Density estimation ; Infinitely divisible distributions ; Kernel estimators ; Lower bounded support
- 刊名：Journal of Statistical Planning and Inference
- 出版年：2012
- 期刊代码：36_03783758
- 类别：mt
- 出版时间：July, 2012
- 卷：142
- 期：7
- 页码：1698-1715
- 文件大小：399 K
摘要
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 . The adaptive estimators are illustrated on simulated data. We compare our approach with the classical kernel estimators.