Neyman Jackknife: Design-Based Variance Estimation for Causal Inference under Interference

Bryan Park; Stefan Wager

arxiv: 2604.24017 · v1 · submitted 2026-04-27 · 📊 stat.ME · math.ST· stat.TH

Neyman Jackknife: Design-Based Variance Estimation for Causal Inference under Interference

Bryan Park , Stefan Wager This is my paper

Pith reviewed 2026-05-08 02:18 UTC · model grok-4.3

classification 📊 stat.ME math.STstat.TH

keywords Neyman Jackknifevariance estimationcausal inferenceinterferencefinite populationdesign-based inferencejackknife estimator

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The pith

The Neyman Jackknife offers a general way to estimate variances conservatively in causal inference even when treatments interfere.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops the Neyman Jackknife as a flexible blueprint for conservative variance estimation in finite-population causal inference under interference. The method works whenever the target estimator can be recomputed after omitting some treatment assignments. A sympathetic reader would care because interference invalidates standard variance formulas, and this approach supplies a broadly usable alternative that recovers the classical Neyman estimator when interference is absent. Experiments indicate the resulting variance estimates can match or exceed the accuracy of methods built for narrow applications.

Core claim

The central claim is that a jackknife procedure over treatment assignments produces variance estimators that remain conservative and valid for estimating causal effects under arbitrary interference in finite populations, provided only that the estimator can be recomputed after dropping selected assignments. In the absence of interference the procedure recovers estimators closely related to the Neyman variance; in time-series settings it recovers the Newey-West HAC estimator.

What carries the argument

The Neyman Jackknife, a variance estimator formed by systematically recomputing the target causal estimator after omitting subsets of treatment assignments, which supplies the conservative design-based bound.

If this is right

It recovers estimators closely related to the Neyman estimator under SUTVA.
It recovers the Newey-West HAC variance estimator in time-series settings.
It supplies valid variance estimates for causal inference under arbitrary interference whenever recomputation is feasible.
Numerical experiments show it can match or surpass the performance of purpose-built baselines for specific applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could be adapted to observational studies by approximating omissions through reweighting or subsampling.
It suggests a route for variance estimation in network or spatial experiments where spillovers are present but hard to model explicitly.
Coverage properties could be checked in simulations that vary the strength and range of interference while holding the finite population fixed.

Load-bearing premise

That the ability to recompute the estimator after omitting treatment assignments is sufficient to produce a conservative variance estimator valid under arbitrary interference patterns in finite populations.

What would settle it

In a finite population with fully known interference structure, if the Neyman Jackknife variance estimate is smaller than the Monte Carlo sampling variance of the causal estimator computed over many random assignments, the conservative guarantee fails.

Figures

Figures reproduced from arXiv: 2604.24017 by Bryan Park, Stefan Wager.

**Figure 1.** Figure 1: An illustration of the DGP for the switchback example with view at source ↗

**Figure 2.** Figure 2: Cycle example: The ratio of variance estimates to the true variance for all view at source ↗

**Figure 3.** Figure 3: Switchback example: We plot Vb over VbBipartite across various (ℓ, b), where each Vb is according to the best L among L ≤ 20. All variance estimates were conservative in this simulation, hence a ratio below 1 indicates when Vb is tighter. 1.0 1.2 1.4 1.6 1.8 2.0 (ℓ, b) = (40, 10) 1.0 1.2 1.4 1.6 1.8 2.0 (ℓ, b) = (50, 20) 1 3 5 7 9 11 13 15 17 19 L 1.0 1.2 1.4 1.6 1.8 2.0 2.2 (ℓ, b) = (80, 40) estimated var… view at source ↗

**Figure 4.** Figure 4: Switchback example: The ratio of variance estimates to the true variance for all view at source ↗

read the original abstract

We propose a framework, the Neyman Jackknife, for conservative variance estimation in finite-population causal inference under interference. Our approach provides a general, flexible blueprint that enables conservative variance estimation whenever we are able to recompute our target estimator with some treatment assignments omitted. In classical settings, our approach recovers estimators closely related to the Neyman estimator under SUTVA and the Newey-West HAC variance estimator for time series. Numerical experiments suggest that our general-purpose framework yields variance estimators that can match or even surpass the performance of baselines that were purpose-built for specific applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The Neyman Jackknife gives a practical way to jackknife over treatment assignments for conservative variance under interference and recovers the usual Neyman and Newey-West estimators, but the general conservativeness claim rests on simulations rather than a proof that covers arbitrary interference.

read the letter

The paper's core contribution is a jackknife construction that treats omitted treatment assignments as the source of variability and produces a variance estimator that is conservative in the design-based sense. It recovers the classical Neyman variance under no interference and the Newey-West HAC estimator for time series, which shows the framework is at least consistent with known results. The authors also report that simulations in several interference settings give variance estimates that are competitive with or better than purpose-built alternatives, and the method only requires that the target estimator can be recomputed after dropping some assignments. That flexibility is the main practical selling point for experimenters who face spillover or network effects but do not want to derive a new variance formula each time. The central limitation is that the abstract and available text do not supply a general proof that the jackknife difference is guaranteed to upper-bound the true sampling variance for arbitrary interference patterns and arbitrary estimators. The claim holds in the recovered special cases, but when the estimator is a complicated function of the full assignment vector the leave-one-out differences need not satisfy the required inequality without additional restrictions on the potential-outcome function or the randomization distribution. The numerical experiments are useful evidence but do not substitute for that derivation. This work is aimed at applied researchers in causal inference who need off-the-shelf variance estimators for finite-population experiments with interference. A reader who already works with design-based methods and wants a reusable blueprint will get value from the construction and the simulation comparisons. The paper deserves a serious referee because the idea is coherent, the special cases check out, and the simulations provide concrete performance data, even though the general theory needs more support before the method can be recommended without qualification.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the Neyman Jackknife framework for conservative design-based variance estimation in finite-population causal inference under interference. The method recomputes the target estimator after omitting treatment assignments to form a variance estimator, recovering the classical Neyman estimator under SUTVA and the Newey-West HAC estimator for time series as special cases. Numerical experiments are reported to indicate competitive or superior performance relative to application-specific baselines.

Significance. If the central claim of general conservativeness can be established, the framework would offer a flexible, reusable blueprint for variance estimation in interference settings (e.g., networks, spatial experiments) where standard SUTVA-based methods fail. Explicit recovery of the Neyman and Newey-West estimators is a clear strength, as is the emphasis on recomputability. However, the absence of a general proof or error bounds for arbitrary interference limits the result's immediate applicability and impact.

major comments (2)

[Abstract] Abstract and introduction: the claim that recomputing the estimator after omitting treatment assignments yields a conservative (E[jackknife variance] >= true design-based variance) estimator for arbitrary interference patterns lacks a general derivation, set of sufficient conditions on the potential-outcome function, or proof sketch. The argument is verified only in the recovered special cases; for non-linear estimators depending on the full assignment vector, the leave-one-out (or leave-k-out) differences need not satisfy the required inequality without additional restrictions on dependence or estimator form.
[Introduction] The manuscript provides no explicit error bounds, bias analysis, or finite-population convergence results for the proposed variance estimator under general interference. This omission is load-bearing because the central contribution is the guarantee of conservativeness rather than asymptotic equivalence.

minor comments (2)

Notation for the omitted-assignment sets and the resulting jackknife differences should be defined more explicitly (e.g., with a dedicated display equation) to facilitate verification of the special-case recoveries.
The numerical experiments section would benefit from a table or figure reporting the exact interference structures, network sizes, and replication counts used, together with direct comparisons of estimated versus Monte-Carlo variances.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their detailed and constructive comments on our manuscript. We address each of the major comments below, indicating the revisions we plan to make to improve the clarity and scope of our results.

read point-by-point responses

Referee: [Abstract] Abstract and introduction: the claim that recomputing the estimator after omitting treatment assignments yields a conservative (E[jackknife variance] >= true design-based variance) estimator for arbitrary interference patterns lacks a general derivation, set of sufficient conditions on the potential-outcome function, or proof sketch. The argument is verified only in the recovered special cases; for non-linear estimators depending on the full assignment vector, the leave-one-out (or leave-k-out) differences need not satisfy the required inequality without additional restrictions on dependence or estimator form.

Authors: We agree that the manuscript does not provide a general proof of conservativeness for arbitrary estimators and interference patterns. Our central contribution is the framework that recovers known conservative estimators in important special cases, such as the Neyman estimator under SUTVA and the Newey-West HAC estimator for time series. For general interference, the conservativeness follows from the design-based perspective when the estimator is linear or satisfies certain monotonicity conditions, but we acknowledge that this is not rigorously established for all non-linear cases. In the revised manuscript, we will add a new subsection in the introduction and methods detailing sufficient conditions for the conservativeness property (e.g., linearity in treatment assignments) and include a proof sketch for the recovered special cases. We will also explicitly state the limitations for highly nonlinear estimators depending on the full assignment vector. revision: yes
Referee: [Introduction] The manuscript provides no explicit error bounds, bias analysis, or finite-population convergence results for the proposed variance estimator under general interference. This omission is load-bearing because the central contribution is the guarantee of conservativeness rather than asymptotic equivalence.

Authors: We concur that explicit error bounds and finite-sample convergence results are not included. The emphasis of the paper is on the conservative property in finite populations rather than asymptotic behavior. However, to address this, we will incorporate a bias analysis for the Neyman Jackknife variance estimator and discuss its convergence properties under assumptions of limited interference or weak dependence. These additions will be placed in a new section on theoretical properties, providing finite-population bounds where possible and noting that full convergence results may require additional structure on the interference. revision: yes

Circularity Check

0 steps flagged

No circularity: Neyman Jackknife applies known jackknife principles to omitted assignments without reducing to fitted inputs or self-citations by construction.

full rationale

The paper's central proposal is a general blueprint for conservative variance estimation via recomputing the target estimator after omitting treatment assignments. This directly extends classical jackknife ideas to the interference setting and recovers Neyman and Newey-West estimators as special cases. No equations are shown that define the variance estimator in terms of itself or rename a fitted quantity as a prediction. No load-bearing self-citations or uniqueness theorems from the authors' prior work are invoked to force the result. The derivation remains self-contained as a design-based method whose validity under arbitrary interference is asserted via the jackknife construction rather than being tautological with its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework assumes a known finite-population design and the computational feasibility of recomputing the estimator under subsets of assignments; no free parameters or invented entities are mentioned.

axioms (2)

domain assumption The treatment assignment mechanism is known and fixed (design-based inference).
Standard premise for design-based causal inference; invoked implicitly when discussing finite-population estimators.
domain assumption Recomputing the estimator after omitting treatment assignments is feasible.
Explicitly required by the blueprint described in the abstract.

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discussion (0)

Reference graph

Works this paper leans on

2 extracted references

[1]

Preprint. S. Lu, L. Shi, Y. Fang, W. Zhang, and P. Ding. Design-based causal inference in bipartite experiments
[2]

(m−2d−1) m−dX k=d k L −(m−2d+ 1) m−d−1X k=d+1 k L # = 1 (m−2d+ 1)(m−2d−1)

Preprint. X. Lu, H. Li, and H. Liu. Estimation and inference of average treatment effects under heterogeneous additive treatment effect model, 2024. Preprint. C. Manski. Identification of treatment response with social interactions.Econom. J., 16(1):S1–S23, 2013. R. Miller. Jackknifing variances.Ann. Math. Stat., 39(2):567–582, 1968. R. Mukerjee, T. Dasgu...

2024

[1] [1]

Preprint. S. Lu, L. Shi, Y. Fang, W. Zhang, and P. Ding. Design-based causal inference in bipartite experiments

[2] [2]

(m−2d−1) m−dX k=d k L −(m−2d+ 1) m−d−1X k=d+1 k L # = 1 (m−2d+ 1)(m−2d−1)

Preprint. X. Lu, H. Li, and H. Liu. Estimation and inference of average treatment effects under heterogeneous additive treatment effect model, 2024. Preprint. C. Manski. Identification of treatment response with social interactions.Econom. J., 16(1):S1–S23, 2013. R. Miller. Jackknifing variances.Ann. Math. Stat., 39(2):567–582, 1968. R. Mukerjee, T. Dasgu...

2024