Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Statistics Theory

arXiv:2204.08402 (math)
[Submitted on 18 Apr 2022 (v1), last revised 19 Jul 2023 (this version, v2)]

Title:Rank Based Tests for High Dimensional White Noise

Authors:Dachuan Chen, Fengyi Song, Long Feng
View PDF
Abstract:The development of high-dimensional white noise test is important in both statistical theories and applications, where the dimension of the time series can be comparable to or exceed the length of the time series. This paper proposes several distribution-free tests using the rank based statistics for testing the high-dimensional white noise, which are robust to the heavy tails and do not quire the finite-order moment assumptions for the sample distributions. Three families of rank based tests are analyzed in this paper, including the simple linear rank statistics, non-degenerate U-statistics and degenerate U-statistics. The asymptotic null distributions and rate optimality are established for each family of these tests. Among these tests, the test based on degenerate U-statistics can also detect the non-linear and non-monotone relationships in the autocorrelations. Moreover, this is the first result on the asymptotic distributions of rank correlation statistics which allowing for the cross-sectional dependence in high dimensional data.
Subjects: Statistics Theory (math.ST); Methodology (stat.ME)
Cite as: arXiv:2204.08402 [math.ST]
  (or arXiv:2204.08402v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2204.08402

Submission history

From: Long Feng [view email]
[v1] Mon, 18 Apr 2022 16:55:28 UTC (242 KB)
[v2] Wed, 19 Jul 2023 04:52:01 UTC (1,041 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
math.ST
< prev   |   next >
new | recent | 2022-04
Change to browse by:
math
stat
stat.ME
stat.TH

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)