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arxiv: 2511.07999 · v3 · submitted 2025-11-11 · 📊 stat.ME

Inference on multiple quantiles in regression models by a rank-score approach

Riccardo De Santis , Anna Vesely , Angela Andreella This is my paper

Pith reviewed 2026-05-17 23:57 UTC · model grok-4.3

classification 📊 stat.ME
keywords quantile regressionmultiple testingrank-score testclosed testingfamilywise error ratemultivariate inferencestatistical power
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The pith

A multivariate rank-score test inside closed testing controls familywise error for multiple quantiles while gaining power over Bonferroni.

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

The paper develops a procedure for simultaneous inference on regression coefficients at several different quantile levels. It creates a multivariate version of the rank-score test and integrates it into a closed-testing framework to manage the overall error rate across all tests. This setup matters for applied work because quantile regression examines effects across the distribution yet separate tests without adjustment can produce excess false positives. If the claims hold, analysts can run multiple quantile analyses with reliable error control and better ability to detect real effects than with standard corrections.

Core claim

The authors extend the rank-score test to the multivariate case for joint testing of quantile regression coefficients across multiple levels and embed the extension in a closed-testing procedure. They further generalize the multivariate test to increase power against alternatives in selected directions. Theory and simulations establish that the resulting method controls the familywise error rate at the nominal level.

What carries the argument

The multivariate extension of the rank-score test placed inside a closed-testing procedure, which jointly evaluates effects at multiple quantiles and adjusts for multiplicity.

If this is right

  • The method keeps the familywise error rate at the desired level when testing multiple quantiles together.
  • Power exceeds that of Bonferroni corrections under the alternatives considered.
  • The directional generalization further improves detection for selected patterns of effects.
  • Simulation results support both error control and the power gain in finite samples.

Where Pith is reading between the lines

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

  • Applied researchers could replace separate Bonferroni-adjusted quantile tests with this procedure to report more effects without inflating overall error.
  • The same closed-testing structure might be adapted to other regression settings that involve multiple related parameters.
  • Direct comparison with false-discovery-rate methods on the same quantile problems would clarify when each approach is preferable.

Load-bearing premise

The rank-score test properties extend to the multivariate setting and the closed-testing procedure applies directly to the quantile regression context without additional unstated conditions on the data or model.

What would settle it

A simulation study in which the observed familywise error rate exceeds the nominal alpha under the global null hypothesis for several quantiles would show the control claim does not hold.

Figures

Figures reproduced from arXiv: 2511.07999 by Angela Andreella, Anna Vesely, Riccardo De Santis.

Figure 1
Figure 1. Figure 1: Tree of intersection hypotheses for three individual hypotheses. Adapted [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Type I error control for Wald-type and generalized rank-score tests with [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Empirical power of the generalized rank-score tests for the 31 intersection [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Empirical power for individual hypotheses. Solid black lines represent the [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Empirical power for individual hypotheses. Solid black lines represent [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
read the original abstract

This paper tackles the challenge of performing multiple quantile regressions across different quantile levels and the associated problem of controlling the familywise error rate, an issue that is generally overlooked in practice. We propose a multivariate extension of the rank-score test and embed it within a closed-testing procedure to efficiently account for multiple testing. Then we further generalize the multivariate test to enhance statistical power against alternatives in selected directions. Theoretical foundations and simulation studies demonstrate that our method effectively controls the familywise error rate while achieving higher power than traditional corrections, such as Bonferroni.

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.

Referee Report

1 major / 2 minor

Summary. The paper proposes a multivariate extension of the rank-score test for simultaneous inference across multiple quantile levels in regression models. This test is embedded in a closed-testing procedure to control the familywise error rate (FWER), with a further generalization to increase power against alternatives in selected directions. Theoretical results on the joint distribution and simulation studies are presented to support FWER control and power gains relative to Bonferroni correction.

Significance. If the central theoretical claims hold, the work provides a less conservative alternative for multiple quantile inference, addressing a gap where FWER control is often ignored in practice. This could improve efficiency in applications such as econometrics or medical statistics that routinely examine effects at several quantiles.

major comments (1)
  1. [§3] §3 (theoretical foundations): The validity of the closed-testing procedure for FWER control rests on the multivariate rank-score test having correct joint size for every intersection hypothesis. The derivation of the joint asymptotic distribution must explicitly justify the off-diagonal covariance terms between score processes at different tau levels; without this, size distortion is possible under heteroskedasticity or dependent errors, undermining the central claim.
minor comments (2)
  1. [Simulation studies] The simulation section would benefit from explicit reporting of the estimated covariance matrices and coverage of the intersection tests under the global null.
  2. [Methods] Notation for the multivariate score vector and its limiting covariance could be introduced earlier and used consistently.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the single major comment below and will incorporate clarifications in the revised version.

read point-by-point responses

  1. Referee: [§3] §3 (theoretical foundations): The validity of the closed-testing procedure for FWER control rests on the multivariate rank-score test having correct joint size for every intersection hypothesis. The derivation of the joint asymptotic distribution must explicitly justify the off-diagonal covariance terms between score processes at different tau levels; without this, size distortion is possible under heteroskedasticity or dependent errors, undermining the central claim.

    Authors: We appreciate the referee's emphasis on this foundational point. Theorem 3.2 establishes the joint asymptotic normality of the vector of rank-score statistics across multiple quantile levels. The off-diagonal covariance terms arise from the limiting covariance of the empirical rank-score processes at distinct τ and τ', which is explicitly expressed as the integral involving the product of the subgradient indicators weighted by the conditional density f(·|x) evaluated at the quantile functions. This construction automatically accommodates heteroskedasticity because the density and the score contributions are allowed to depend on covariates. The derivation relies on the uniform consistency of the quantile estimators and the weak convergence of the associated empirical processes under standard regularity conditions (independent observations with finite moments). We agree that the current presentation of these cross-covariance terms could be expanded for greater transparency. In the revision we will add a dedicated remark and an appendix that walks through the calculation of the off-diagonal elements step by step, including the explicit form under heteroskedasticity. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on independent asymptotic theory and closed-testing framework

full rationale

The paper proposes a multivariate extension of the rank-score test embedded in closed testing for FWER control across quantiles. No quoted step reduces a claimed result to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation whose validity is presupposed without external verification. The abstract and described theoretical foundations present the joint distribution and closed-testing application as derived from standard rank-score asymptotics and established multiple-testing procedures, without renaming known results or smuggling ansatzes via self-citation. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit list of free parameters, axioms, or invented entities; the approach appears to rest on standard assumptions of quantile regression and rank-score tests.

pith-pipeline@v0.9.0 · 5379 in / 1063 out tokens · 25729 ms · 2026-05-17T23:57:49.147221+00:00 · methodology

discussion (0)

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Reference graph

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