ADAPTIVE ESTIMATION FOR HAWKES PROCESSES; APPLICATION TO GENOME ANALYSIS

• 成果类型: Article
• 署名作者: Reynaud-Bouret, Patricia; Schbath, Sophie
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite Paris Saclay; INRAE
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS806
• 发表日期: 2010
• 页码: 2781-2822
• 关键词: poisson; penalties; intensity

摘要

The aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex enough to need a nonasymptotic penalized model selection approach. We provide a theoretical penalty that satisfies an oracle inequality even for quite complex families of models. The consecutive theoretical estimator is shown to be adaptive minimax for Holderian functions with regularity in (1/2, 1]: those aspects have not yet been studied for the Hawkes' process. Moreover, we introduce an efficient strategy, named Islands, which is not classically used in model selection, but that happens to be particularly relevant to the biological question we want to answer. Since a multiplicative constant in the theoretical penalty is not computable in practice, we provide extensive simulations to find a data-driven calibration of this constant. The results obtained on real genomic data are coherent with biological knowledge and eventually refine them.