Pith Number

pith:BSAWYPEJ

pith:2026:BSAWYPEJXQLJI77GD6OLUMLLE2

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Goodness-of-Fit Testing for Point Processes in Large Populations

Estate V. Khmaladze, Roger J. A. Laeven, Sami Umut Can

A unitary transformation maps the natural testing process for parametric point processes to a limiting target whose distribution is free of unknown intensity parameters.

arxiv:2605.15814 v1 · 2026-05-15 · math.ST · stat.TH

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Claims

C1strongest claim

We propose a novel approach to conducting such goodness-of-fit tests. The idea is to construct a unitary transformation of a natural parametric testing process such that it converges weakly to a ``standard'' target process, independent of the particular parametric form assumed under the null hypothesis. This transformation therefore paves the way for asymptotically distribution-free goodness-of-fit testing of parametric point processes.

C2weakest assumption

The assumption that a unitary transformation exists which maps the natural parametric testing process to a limiting target whose distribution is completely free of the unknown parameters in the intensity family; this premise is invoked when the abstract states that the transformed process converges weakly to a standard target independent of the parametric form.

C3one line summary

A unitary transformation is introduced for parametric testing processes in point processes to enable asymptotically distribution-free goodness-of-fit tests.

References

70 extracted · 70 resolved · 0 Pith anchors

[1] 2002 , PUBLISHER = 2002

[2] 1996 , PUBLISHER = 1996

[3] 2007 , PUBLISHER = 2007

[4] Lin, D. and Wei, L.-J. and Ying, Z. , JOURNAL =. Checking the

[5] and Dobler, Dennis and de Gunst, Mathisca C

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:19.922142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c816c3c89bc16947fe61f9cba316b26897d4534cb2b23ed2c5c6db8a04ea631

Aliases

arxiv: 2605.15814 · arxiv_version: 2605.15814v1 · doi: 10.48550/arxiv.2605.15814 · pith_short_12: BSAWYPEJXQLJ · pith_short_16: BSAWYPEJXQLJI77G · pith_short_8: BSAWYPEJ

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/BSAWYPEJXQLJI77GD6OLUMLLE2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0c816c3c89bc16947fe61f9cba316b26897d4534cb2b23ed2c5c6db8a04ea631

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f9f6f0a6982ce8f0617694e91bc8ca8d3ccc53d76dcfa10f8c9bd8147baca74",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-15T10:09:49Z",
    "title_canon_sha256": "a913d227e8f0649f72679a8a3290f9dfb41d2ba8774c3c613752dd7a3bf89e2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15814",
    "kind": "arxiv",
    "version": 1
  }
}