Paper Citation Record · LEDGER

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift

As of 9 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2506.23453.

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pith.paper-citation-record.v1
2506.23453 v1

Coverage vector

measured 22 of 22 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-06T21:56:38.803789Z

measured 22 of 22 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

22 of 22 outbound references displayed

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verified fuzzy17
unresolved5
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External citation measurements

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Outbound references

Observation 6feefa65-3a7c-46cb-8257-2307caf51f02 · outbound

This paper cites In order to determine the separation between two priors µ0 and µ1, we need to derive the con- centration inequality of each prior first.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift In order to determine the separation between two priors µ0 and µ1, we need to derive the con- centration inequality of each prior first

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:40.412038Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6c6d15de-a800-4360-8ad3-44dcb0b75bf9 · outbound

This paper cites of the uniform distribution over [0, 1]d.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift of the uniform distribution over [0, 1]d

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:40.552070Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d9cb1dca-fd75-465f-93c7-55bdd611e4ae · outbound

This paper cites A.5 P ROOF OF COROLLARY 1 Corollary 1 (Double Robustness of Plug-in Truncated Estimator).

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift A.5 P ROOF OF COROLLARY 1 Corollary 1 (Double Robustness of Plug-in Truncated Estimator)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.716500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0c04e898-49d7-4244-a6b8-bde1175c47a8 · outbound

This paper cites Instance weighting for neural machine translation domain adaptation.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Instance weighting for neural machine translation domain adaptation

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:40.944528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a361389f-eed9-4ed4-b637-3e9d1af7e279 · outbound

This paper cites an unresolved cited work.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:56:40.699998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7b6872e1-69a2-45e3-b116-e198f5a4c0c5 · outbound

This paper cites Assume that p ≥ 2, q ≤ p ≤ 2q and s d > 1 p − 1 2q.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Assume that p ≥ 2, q ≤ p ≤ 2q and s d > 1 p − 1 2q

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:40.261221Z

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Observation b640e6d5-f911-4633-81b1-e11e975bb19d · outbound

This paper cites This gives us the final upper bound under the assumption that s ∈ ( d(2q−p) p(2q−2) , d p ) as follows: ES1 Z Ω g2 S1 (x)f 2q−2(x) dx ≲ ¯b · n− 2s d.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift This gives us the final upper bound under the assumption that s ∈ ( d(2q−p) p(2q−2) , d p ) as follows: ES1 Z Ω g2 S1 (x)f 2q−2(x) dx ≲ ¯b · n− 2s d

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:40.106720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2e70dd0a-0a45-49fe-997f-7e1c1eb6fc49 · outbound

This paper cites (22) Combining the upper bounds derived in 19 20, 21 and 22 we may deduce that: ES1 ES2|S1 f q(X) − ˆf q S1 (X) 2 ≲ ¯b2 · h n2q( 1 p − s d )−1 + max{n− 2s d , n2q( 1 p − s d )−1} i.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift (22) Combining the upper bounds derived in 19 20, 21 and 22 we may deduce that: ES1 ES2|S1 f q(X) − ˆf q S1 (X) 2 ≲ ¯b2 · h n2q( 1 p − s d )−1 + max{n− 2s d , n2q( 1 p − s d )−1} i

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.978815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2fc3fc5e-3bb5-4035-8c9c-6f4a87fdc86e · outbound

This paper cites Z Ω− T p∗(x) ˆf q S1 (x)dx + Z Ω− T T p◦(x) · (f q(x) − ˆf q S1 (x))dx − Z Ω− T p∗(x)f q(x)dx # =ES1.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Z Ω− T p∗(x) ˆf q S1 (x)dx + Z Ω− T T p◦(x) · (f q(x) − ˆf q S1 (x))dx − Z Ω− T p∗(x)f q(x)dx # =ES1

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.820047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 95d112a6-1223-4b35-a70b-602435a1abf0 · outbound

This paper cites To estimate the propensity score, we can apply a classification model that distinguishes between source and target samples.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift To estimate the propensity score, we can apply a classification model that distinguishes between source and target samples

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.538018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 22e52dd3-9e65-4ff9-9f70-e9f4a5f5917e · outbound

This paper cites These potential outcomes are un- known functions of the covariate X.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift These potential outcomes are un- known functions of the covariate X

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.441606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f4890b1c-4f8a-4847-9352-6ae17f095e37 · outbound

This paper cites (8) may outperform the minimax lower bound B · ¯b · r(n) when B is large.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift (8) may outperform the minimax lower bound B · ¯b · r(n) when B is large

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.339858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d0fe20f7-3753-43f0-9754-d79ff813c8f0 · outbound

This paper cites • ux(y) = 0 for any y ∈ Ω and x ∈ P with ∥x − y∥ ≥a2ρ(P, Ω).

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift • ux(y) = 0 for any y ∈ Ω and x ∈ P with ∥x − y∥ ≥a2ρ(P, Ω)

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.191809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8a5aa1d5-6fac-4459-88c9-de2fe9e499d8 · outbound

This paper cites However, as B increases, the two-stage estimator demonstrates greater accuracy and improved stability, highlighting its necessity under significant covariate shift.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift However, as B increases, the two-stage estimator demonstrates greater accuracy and improved stability, highlighting its necessity under significant covariate shift

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:39.036114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8766d500-bd09-4ee0-858c-c1c4431866f0 · outbound

This paper cites Analysis of Kernel Mean Matching under Covariate Shift.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Analysis of Kernel Mean Matching under Covariate Shift

Reference 2004

Resolution: unresolved; no resolver link, observed 2026-08-06T21:56:37.804856Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad9bd3ba-f069-41ad-8162-11f2c7c6c251 · outbound

This paper cites Let Hf,q n denote the class of all the estimators using S = {(xi, yi = f (xi))}n i=1 to estimate the q-th moment of f under P∗.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Let Hf,q n denote the class of all the estimators using S = {(xi, yi = f (xi))}n i=1 to estimate the q-th moment of f under P∗

Reference 2012

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:40.856258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f06fe8ee-5e32-44e9-89e8-19fda4edf8fb · outbound

This paper cites The covering radius of randomly distributed points on a manifold.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift The covering radius of randomly distributed points on a manifold

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:41.241936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 05e66ff0-b56a-4f9d-9f1b-26907c01d088 · outbound

This paper cites Optimal transport for treatment effect estimation.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Optimal transport for treatment effect estimation

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:41.119802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f21f7ed2-3786-4a8a-b477-a5285d6342a1 · outbound

This paper cites BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-06T21:56:37.321987Z

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Unavailable: canonical work link unavailable.

Observation 37e1c9eb-981d-499c-929a-db208374ba7d · outbound

This paper cites Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-06T21:56:37.430303Z

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Observation ffdfb181-73b3-4e77-ad6b-89882880da54 · outbound

This paper cites Lipschitz density-ratios, structured data, and data-driven tuning.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Lipschitz density-ratios, structured data, and data-driven tuning

Reference 2023

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:56:41.371556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4a39a379-0935-4ff3-84f4-edec64edd661 · outbound

This paper cites Few-Shot Learning via Learning the Representation, Provably.

Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift Few-Shot Learning via Learning the Representation, Provably

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-06T21:56:37.375139Z

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