Pith Number

pith:TFVTTZHX

pith:2026:TFVTTZHXQAMV46LKTR4YWZFSDW

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Predictive Inference via Kernel Density Estimates

Torey Hilbert

Kernel density estimator and recursive kernel predictive processes converge weakly almost surely, with the classic version limiting to compact support and the recursive version to non-compact support.

arxiv:2605.14008 v1 · 2026-05-13 · stat.ME · math.ST · stat.TH

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Claims

C1strongest claim

We show that both processes converge weakly almost surely, which opens the door for new Bayesian interpretations of kernel density estimation. Surprisingly, the process based on the classic kernel density estimates converges to a compactly supported measure, while the recursive version converges to a non-compactly supported measure.

C2weakest assumption

The underlying data are i.i.d. draws from an unknown distribution, and the kernel and bandwidth sequence satisfy standard regularity conditions that enable weak convergence of the predictive processes.

C3one line summary

References

16 extracted · 16 resolved · 1 Pith anchors

[1] Journal of the Royal Statistical Society Series B: Statistical Methodology , volume= 2023

[2] Statistical Science , volume= 2025

[3] Bayesian predictive inference beyond martingales

[4] The Annals of Probability , number =

[5] Kernel based Dirichlet sequences , author=. Bernoulli , volume=. 2023 , publisher= 2023

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:13.089671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

996b39e4f780195e796a9c798b64b21d8eb88e7bc428bc99fe4809215f04a1be

Aliases

arxiv: 2605.14008 · arxiv_version: 2605.14008v1 · doi: 10.48550/arxiv.2605.14008 · pith_short_12: TFVTTZHXQAMV · pith_short_16: TFVTTZHXQAMV46LK · pith_short_8: TFVTTZHX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TFVTTZHXQAMV46LKTR4YWZFSDW \
  | 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: 996b39e4f780195e796a9c798b64b21d8eb88e7bc428bc99fe4809215f04a1be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29e7e1728cf2ccac9783df4dc5e28fc800fd51fbb4b86a1dc7d6da3f3ef406d8",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T18:13:03Z",
    "title_canon_sha256": "07630e42fe917d2d6ce11646b39b65e9e7e8f30379033b4945b35e2840b5e8e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14008",
    "kind": "arxiv",
    "version": 1
  }
}