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A High-Dimensional LM Test for Cross-Sectional Independence with Serially Correlated Data — arXiv:2611.02308

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02308
License (as archived): CC0-1.0
Archived: 2026-11-03T11:33:39.911Z
SHA-256 of the archived text: e6c7a2710e1539d53caa72e92ee44ad5ef7ab5b3ba2a9ea71db1aeb8155eabc1
Stable URL of this page: https://metraipolis.com/documento/dc_fa90bc0fc41e

How to cite

A High-Dimensional LM Test for Cross-Sectional Independence with Serially Correlated Data — arXiv:2611.02308 — arXiv (en), https://arxiv.org/abs/2611.02308 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fa90bc0fc41e (Metraipolis archive dc_fa90bc0fc41e, sha256 e6c7a2710e1539d53caa72e92ee44ad5ef7ab5b3ba2a9ea71db1aeb8155eabc1)

BibTeX

@misc{dcfa90bc0fc41e,
  title = {A High-Dimensional LM Test for Cross-Sectional Independence with Serially Correlated Data — arXiv:2611.02308},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02308},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fa90bc0fc41e; sha256 e6c7a2710e1539d53caa72e92ee44ad5ef7ab5b3ba2a9ea71db1aeb8155eabc1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02308. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop a high-dimensional Lagrange multiplier (LM) test for cross-sectional independence in Gaussian panels with a common stationary, short-memory temporal covariance matrix. The statistic is based on the trace of the square of R, where R is the sample correlation matrix. When the cross-sectional and time dimensions grow proportionally, we derive explicit expansions for the null mean and variance in terms of temporal spectral moments. Random diagonal normalization produces a non-negligible centering correction, while squared sample correlations sharing a cross-sectional unit contribute an additional variance term. Both corrections vanish under temporal independence. We establish a central limit theorem under the null, consistency against fixed alternatives, and a Gaussian-shift limit with a detection boundary under local alternatives. Monte Carlo experiments examine the size and power of the oracle test and feasible versions that estimate the temporal spectral moments. The asymptotic theory applies to the oracle statistic; feasible procedures are evaluated numerically.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2611.02308 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:04:37.201Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).