Poisson点过程的一致反褶积
Uniform Deconvolution for Poisson Point Processes
摘要：
本文主要研究在均匀噪声背景下泊松过程的强度估计问题。我们提出了一个基于内核的程序完全校准的理论和实践。我们表明，我们的自适应估计是最佳的甲骨文和极大极小的观点，并提供新的下界时，强度属于一个Sobolev球。通过发展的Goldenshluger-Lepski方法的情况下，泊松过程的反卷积，我们提出了一个最佳的数据驱动的核带宽的选择。我们的方法说明了沿人类基因组的复制起点和序列基序的空间分布。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
