论文标题
泊松点过程的统一反卷积
Uniform Deconvolution for Poisson Point Processes
论文作者
论文摘要
我们专注于在存在均匀噪声的情况下对泊松过程强度的估计。我们提出了一个基于内核的程序，可以完全校准理论和实践中。我们表明，从Oracle和Minimax的角度来看，自适应估计器是最佳的，当强度属于Sobolev Ball时提供新的下限。通过开发Goldenshluger-Lepski方法，在泊松过程的反卷积的情况下，我们提出了核带宽的最佳数据驱动选择。我们的方法在人类基因组沿着复制起源和序列基序的空间分布进行了说明。
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.
