Multiresolution analysis of point processes and statistical thresholding for Haar wavelet-based intensity estimation
| Autor: | Youssef Taleb, Edward A. K. Cohen |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
business.industry Statistics & Probability Homogeneity (statistics) Multiresolution analysis 0104 Statistics 05 social sciences Estimator Pattern recognition 01 natural sciences Thresholding Point process Haar wavelet 010104 statistics & probability Wavelet Likelihood-ratio test 0502 economics and business Artificial intelligence 0101 mathematics business 050205 econometrics Mathematics |
| Zdroj: | Annals of the Institute of Statistical Mathematics. 73:395-423 |
| ISSN: | 1572-9052 0020-3157 |
| Popis: | 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 Haar wavelet 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 process' 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 outperform the existing local hard thresholding strategy on a range of simulation scenarios. The presented methodology is applied to NetFlow data to demonstrate its effectiveness at characterizing multiscale behavior on computer networks. |
| Databáze: | OpenAIRE |
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