Pith Number

pith:WGRJXBIQ

pith:2026:WGRJXBIQCNJRFRB3X524ASSECF

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Nonparametric inference for sublevel-set probabilities of conditional average treatment effect functions

Anders Munch, Thomas A. Gerds

The probability that a conditional average treatment effect falls below a given threshold produces a monotone curve summarizing treatment heterogeneity.

arxiv:2605.15373 v1 · 2026-05-14 · stat.ME

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\usepackage{pith}
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Claims

C1strongest claim

The probability of a sublevel set of a CATE function is a single number with a simple interpretation as the proportion of individuals whose expected treatment effect does not exceed a prespecified threshold. By varying the threshold, a univariate monotone curve appears which can be used to visualize the overall type and degree of heterogeneity in a population. We formalize this curve as a target parameter and show that it is not pathwise differentiable under a nonparametric model.

C2weakest assumption

The CATE function is identifiable from observed data under randomized treatment assignment, allowing the sublevel-set probabilities to be targeted and estimated via monotone function techniques combined with machine learning, as used in the numerical studies based on synthesized randomized trial data.

C3one line summary

Develops Grenander-type and debiased machine learning estimators for the sublevel-set probability curve of the CATE function, shown to be non-pathwise differentiable, along with its piecewise linear approximation.

References

64 extracted · 64 resolved · 0 Pith anchors

[1] J.-Y. Audibert and A. B. Tsybakov. Fast learning rates for plug-in classifiers. The Annals of Statistics, 2007 2007

[2] P. J. Bickel, C. A. Klaassen, Y. Ritov, and J. A. Wellner. Efficient and adaptive estimation for semiparametric models, volume 4. Johns Hopkins University Press Baltimore, 1993 1993

[3] arXiv preprint arXiv:2306.17464 , year= 2023

[4] L. Breiman. Stacked regressions. Machine learning, 24 0 (1): 0 49--64, 1996 1996

[5] Random forests 2001 · doi:10.1023/a:1010933404324

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:55.114656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1a29b8510135312c43bbf75c04a44114d27d3d22a66b2392c92a6aaa480b12d

Aliases

arxiv: 2605.15373 · arxiv_version: 2605.15373v1 · doi: 10.48550/arxiv.2605.15373 · pith_short_12: WGRJXBIQCNJR · pith_short_16: WGRJXBIQCNJRFRB3 · pith_short_8: WGRJXBIQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WGRJXBIQCNJRFRB3X524ASSECF \
  | 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: b1a29b8510135312c43bbf75c04a44114d27d3d22a66b2392c92a6aaa480b12d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cecc431fb007406f9897ace16ef658ac8a3f341c383f73d4950587ef5c5f8205",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-14T20:01:21Z",
    "title_canon_sha256": "31486c61816a560bc6952bfaf978eb18ed15e3116ed6aa91c5ab60e54f8ef541"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15373",
    "kind": "arxiv",
    "version": 1
  }
}