The Annals of Statistics
- Ann. Statist.
- Volume 47, Number 3 (2019), 1754-1775.
Super-resolution estimation of cyclic arrival rates
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.
Ann. Statist., Volume 47, Number 3 (2019), 1754-1775.
Received: June 2017
Revised: June 2018
First available in Project Euclid: 13 February 2019
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Chen, Ningyuan; Lee, Donald K. K.; Negahban, Sahand N. Super-resolution estimation of cyclic arrival rates. Ann. Statist. 47 (2019), no. 3, 1754--1775. doi:10.1214/18-AOS1736. https://projecteuclid.org/euclid.aos/1550026856
- Proofs and asymptotic normality. The proofs of all results presented in this paper are provided in Appendix A of the supplement. Appendix B establishes the asymptotic normality of the windowed periodogram estimator.