# Multiresolution analysis of point processes and statistical thresholding for wavelet-based intensity estimation

arXiv: https://arxiv.org/abs/1803.11202 · HTML: https://mlsanity.com/paper/1803.11202/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2018.

## Built on by (most cited first, 2 of 2)

- [Multiresolution Analysis and Statistical Thresholding on Dynamic Networks](https://mlsanity.com/paper/2506.01208/) (2025)
- [Non-Negative Matrix Factorization for Event Data](https://mlsanity.com/paper/2606.06205/) (2026)

## Abstract (arXiv)

We take a wavelet based approach to the analysis of point processes and the estimation of the first order intensity under a continuous time setting. A multiresolution analysis of a point process is formulated which motivates the definition of homogeneity at different scales of resolution, termed J-th level homogeneity. Further to this, the activity in a point processes' first order behavior at different scales of resolution is also defined and termed L-th level innovation. Likelihood ratio tests for both these properties are proposed with asymptotic distributions provided, even when only a single realization of the point process is observed. The test for L-th level innovation forms the basis for a collection of statistical strategies for thresholding coefficients in a wavelet based estimator of the intensity function. These thresholding strategies are shown to outperform the existing local hard thresholding strategy on a range of simulation scenarios.