Super-resolution Estimation of Cyclic Arrival Rates

Annals of Statistics 47:3:1754-1775 (2019)

32 Pages Posted: 28 Oct 2016 Last revised: 1 Mar 2019

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Donald Lee

Emory University - Goizueta Business School

Sahand Negahban

Yale University

Date Written: September 12, 2016

Abstract

Exploiting the fact that most arrival processes exhibit cyclic behaviour, we propose a simple procedure for estimating the intensity of a non-homogeneous Poisson process. The estimator is the super-resolution analogue to Shao 2010 and Shao & Lii 2011, which is a sum of p sinusoids where p and the frequency, 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.

Keywords: arrival rate estimation; spectral estimation; super-resolution frequency recovery; periodogram; window function; thresholding; nonhomogeneous Poisson process; queueing theory

JEL Classification: C15, C22, C32, C44, C53

Suggested Citation

Chen, Ningyuan and Lee, Donald and Negahban, Sahand, Super-resolution Estimation of Cyclic Arrival Rates (September 12, 2016). Annals of Statistics 47:3:1754-1775 (2019). Available at SSRN: https://ssrn.com/abstract=2840552 or http://dx.doi.org/10.2139/ssrn.2840552

Ningyuan Chen

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Donald Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Sahand Negahban

Yale University ( email )

New Haven, CT 06520
United States

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