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June 2019 Super-resolution estimation of cyclic arrival rates
Ningyuan Chen, Donald K. K. Lee, Sahand N. Negahban
Ann. Statist. 47(3): 1754-1775 (June 2019). DOI: 10.1214/18-AOS1736

Abstract

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.

Citation

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Ningyuan Chen. Donald K. K. Lee. Sahand N. Negahban. "Super-resolution estimation of cyclic arrival rates." Ann. Statist. 47 (3) 1754 - 1775, June 2019. https://doi.org/10.1214/18-AOS1736

Information

Received: 1 June 2017; Revised: 1 June 2018; Published: June 2019
First available in Project Euclid: 13 February 2019

zbMATH: 07053525
MathSciNet: MR3911129
Digital Object Identifier: 10.1214/18-AOS1736

Subjects:
Primary: 62M15 , 90B22
Secondary: 60G55

Keywords: nonhomogeneous Poisson process , periodogram , Queueing theory , spectral estimation , thresholding , window function

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • June 2019
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