We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle and minimax points of view, and provide new lower bounds when the intensity belongs to a Sobolev ball. By developing the Goldenshluger-Lepski methodology in the case of deconvolution for Poisson processes, we propose an optimal data-driven selection of the kernel bandwidth. Our method is illustrated on the spatial distribution of replication origins and sequence motifs along the human genome.
翻译:我们的重点是在出现统一噪音的情况下估计 Poisson 过程的强度。 我们提议一个在理论和实践上完全校准的内核程序。 我们显示我们的适应性测算器从神器和微缩角度是最佳的,当强度属于Sobolev球时,我们提供了新的下限。 通过开发Goldshluger-Lepski方法,在Poisson 过程分解的情况下,我们建议以数据驱动的最佳选择内核带宽。我们的方法用复制源的空间分布和人类基因组的序列模型来说明。