Super-resolution estimation of cyclic arrival rates
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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 & 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. A novel aspect of our approach is the use of window functions with fast decaying spectral tails, which we show is the key to super-resolution in our procedure. Interestingly the prolate spheriodal window that is usually considered optimal in signal processing is suboptimal for frequency recovery. 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.
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