2018/03/29 by Youssef Taleb, Taleb, Youssef, Edward A. K. Cohen +1
Chemistry · Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Methodology (stat.ME) #Spectroscopy and Chemometric Analyses #Statistical and numerical algorithms #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1803.11202
openalex publication_date 2018/03/29 · openalex created_date 2018/04/06 · openalex updated_date 2026/07/28
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.