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TSHT Two-Stage Hard Thresholding with Plurality Voting for Invalid Instruments

Mathematical Methods AIMech:TSHTTwoStageHardThresholdingWithPluralityVotingForInvalidInstruments DRAFT

Aliases: TSHT with Plurality Voting, Two-Stage Hard Thresholding with Voting for Invalid Instruments, TSHT Instrumental Variable Estimator

An instrumental variable causal inference and confidence interval construction method for settings with invalid instruments that first applies hard thresholding to first-stage exposure-instrument regression coefficients (or high-dimensional debiased Lasso estimates) to select relevant instruments, and second applies pairwise hard thresholding to candidate invalidity residuals to construct a symmetric voting matrix whose plurality winner identifies the set of valid instruments for post-selection causal effect estimation.

Identity Notes & Concept Scope No AIO class represents Two-Stage Hard Thresholding with Plurality Voting for invalid instrumental variables; LinearRegression (AIO:LinearRegression) is the closest broad match covering linear instrumental variable regression models.

Claims & Grounded Evidence

4 Claims

Mechanism #plurality-rule-causal-effect-identification

Under the plurality rule (Condition IN1-P), the causal effect beta^* is uniquely identified whenever the set of valid relevant instruments S^* = {j in S : pi_j^* = 0} is strictly larger than any cluster of invalid relevant instruments sharing a common non-zero ratio pi_j^* / gamma_j^* = c != 0 (Theorem 1), strictly relaxing the 50% majority validity requirement.

supports Source: Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting · Locator: Section 2.2, Condition IN1-P and Theorem 1, pp. 6-7

Mechanism #two-stage-hard-thresholding-and-symmetric-voting-matrix

Stage 1 selects strong relevant instruments S_hat by hard thresholding first-stage estimates |gamma_hat_j| against a noise-calibrated threshold (Equations 5-6), and Stage 2 evaluates each candidate beta^[j] = Gamma_hat_j / gamma_hat_j across all k in S_hat by hard thresholding the invalidity residual Gamma_hat_k - beta^[j] gamma_hat_k to form a symmetric binary voting matrix V_hat and select the plurality winner S_hat_V (Equations 7-12).

supports Source: Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting · Locator: Section 3.2-3.5, Equations 5-12, pp. 8-11

Application #mendelian-randomization-and-econometric-iv-application

TSHT with voting is applied to construct asymptotically valid confidence intervals for causal effects in low- and high-dimensional instrumental variable regressions and Mendelian randomization studies with pleiotropic genetic variants.

supports Source: Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting · Locator: Section 3.7, Equations 13-17, pp. 12-14; Section 5-6, pp. 19-28

Limitation #plurality-violation-and-weak-instrument-screening-limitation

TSHT requires the plurality rule (Condition IN1-P) and sufficient first-stage instrument strength to pass Stage 1 hard thresholding; if a coordinated pleiotropic mechanism causes a single non-zero ratio c != 0 to outnumber the valid instruments, or if valid instruments are too weak to survive Stage 1 screening, TSHT can select an invalid cluster.

supports Source: Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting · Locator: Section 2.2, p. 6; Section 3.2, p. 9; Section 4.1, Theorem 2 conditions, pp. 14-16

⚠️ Curated Limitations & Negative Results

TSHT requires the plurality rule (Condition IN1-P) and sufficient first-stage instrument strength to pass Stage 1 hard thresholding; if a coordinated pleiotropic mechanism causes a single non-zero ratio c != 0 to outnumber the valid instruments, or if valid instruments are too weak to survive Stage 1 screening, TSHT can select an invalid cluster.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:LinearRegression` Linear Regression	broad_match	TSHT with plurality voting estimates linear structural causal effects via two-stage hard thresholding and post-selection two-stage least squares regression.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`r832-primary-pdf`	Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting Zijian Guo, Hyunseung Kang, T. Tony Cai, Dylan S. Small	primary paper full_text	ID: https://arxiv.org/abs/1603.05224 sha256:0ef075b24ff2…
`r832-arxiv-abs`	Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting (arXiv abstract) Zijian Guo, Hyunseung Kang, T. Tony Cai, Dylan S. Small	primary paper abstract_only	ID: https://arxiv.org/abs/1603.05224 sha256:ba281d12dc1e…
`r832-metadata-cr`	Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting (Crossref metadata) Zijian Guo, Hyunseung Kang, T. Tony Cai, Dylan S. Small	primary paper abstract_only	ID: https://arxiv.org/abs/1603.05224 sha256:5ddf18480264…

Ontology & Grounding Topology

Open in interactive network graph →

Curation Provenance

Curator: Antigravity

Method: ai_assisted

Model: Gemini

Created: 2026-10-19T15:15:00Z

Updated: 2026-10-19T15:15:00Z

Source File: data/curated/TSHTTwoStageHardThresholdingWithPluralityVotingForInvalidInstruments.yaml · Schema: curated_concept.yaml

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