Pith Number

pith:D2T4AT7R

pith:2026:D2T4AT7RFGQZKAJKZFCMHD7IJS

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Exact Likelihood Inference and Robust Filtering for Gauss-Cauchy Convolution Models

Chen Tong, Peter Reinhard Hansen

Exact analytical expressions for the Gauss-Cauchy convolution density enable stable maximum likelihood estimation and robust filtering in state-space models.

arxiv:2605.01665 v2 · 2026-05-03 · econ.EM · stat.ME

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Claims

C1strongest claim

We derive analytical expressions for its density, score, Hessian, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations.

C2weakest assumption

The measurement noise follows exactly the Gauss-Cauchy convolution distribution and the scaled complementary error function remains numerically stable across all relevant parameter values encountered in estimation and filtering.

C3one line summary

Exact analytical likelihood inference and a redescending robust filter are derived for Gauss-Cauchy convolution models.

Cited by

1 paper in Pith

Tweedie's Formula and Score-Driven Updating

Receipt and verification

First computed	2026-05-29T01:05:11.397737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ea7c04ff129a195012ac944c38fe84cbe5960e8ea11b79ffdb3167685a147c8

Aliases

arxiv: 2605.01665 · arxiv_version: 2605.01665v2 · doi: 10.48550/arxiv.2605.01665 · pith_short_12: D2T4AT7RFGQZ · pith_short_16: D2T4AT7RFGQZKAJK · pith_short_8: D2T4AT7R

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D2T4AT7RFGQZKAJKZFCMHD7IJS \
  | 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: 1ea7c04ff129a195012ac944c38fe84cbe5960e8ea11b79ffdb3167685a147c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74cc9d031a150c0317864e92edb364d1e2e853b3210ef80b6048f1ea92724b36",
    "cross_cats_sorted": [
      "stat.ME"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.EM",
    "submitted_at": "2026-05-03T01:34:26Z",
    "title_canon_sha256": "9f1a1b4f911f15c3e80192099a9dc6dfc9688b8cfa675a740b1ffe28398a0793"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01665",
    "kind": "arxiv",
    "version": 2
  }
}