SUPER-RESOLUTION ESTIMATION OF CYCLIC ARRIVAL RATES

• 成果类型: Article
• 署名作者: Chen, Ningyuan; Lee, Donald K. K.; Negahban, Sahand N.
• 署名单位: Hong Kong University of Science & Technology; Hong Kong University of Science & Technology; Yale University; Yale University; Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1736
• 发表日期: 2019
• 页码: 1754-1775
• 关键词: spectral-analysis; period

摘要

Exploiting the fact that most arrival processes exhibit cyclic behaviour, we propose a simple procedure for estimating the intensity of a nonhomogeneous Poisson process. The estimator is the super-resolution analogue to Shao (2010) and Shao and Lii [J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 (2011) 99-122], which is a sum of p sinusoids where p and the amplitude and phase of each wave are not known and need to be estimated. This results in an interpretable yet flexible specification that is suitable for use in modelling as well as in high resolution simulations. Our estimation procedure sits in between classic periodogram methods and atomic/total variation norm thresholding. Through a novel use of window functions in the point process domain, our approach attains super-resolution without semidefinite programming Under suitable conditions, finite sample guarantees can be derived for our procedure. These resolve some open questions and expand existing results in spectral estimation literature.