Statistical depth for point process via the isometric log-ratio transformation

Xinyu Zhou, Yijia Ma and Wei Wu

Computational Statistics & Data Analysis, 2023, vol. 187, issue C

Abstract: Statistical depth, a useful tool to measure the center-outward rank of multivariate and functional data, is still under-explored in temporal point processes. Recent studies on point process depth proposed a weighted product of two terms - one indicates the depth of the cardinality of the process, and the other characterizes the conditional depth of the temporal events given the cardinality. The second term is of great challenge because of the apparent nonlinear structure of event times, and so far only parametric representations such as Gaussian and Dirichlet densities have been adopted in the definitions. However, these parametric forms ignore the underlying distribution of the process events and are difficult to apply to complicated patterns. To deal with these problems, a novel distribution-based approach is proposed to the conditional depth via the well-known Isometric Log-Ratio (ILR) transformation on the inter-event times. Motivated by a uniform distribution on simplex, the new method, called the ILR depth, is formally defined for general point process via a Time Rescaling. The mathematical properties of the ILR depth are thoroughly examined and the new method is well illustrated by using Poisson and non-Poisson processes to demonstrate its superiority over previous methods. Finally, the ILR depth is applied in a real dataset and the result clearly shows its effectiveness in ranking.

Keywords: Statistical depth; Point process; Isometric log-ratio transformation; Poisson process; Time rescaling (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016794732300124X
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:187:y:2023:i:c:s016794732300124x

DOI: 10.1016/j.csda.2023.107813

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().