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arxiv: 2605.17763 · v1 · pith:MHYELPMPnew · submitted 2026-05-18 · 📊 stat.ME · stat.ML

Comparing Two Categorical Gini Correlations with Applications to Classification Problems

Sameera Hewage , Yongli Sang This is my paper

Pith reviewed 2026-05-20 01:43 UTC · model grok-4.3

classification 📊 stat.ME stat.ML
keywords categorical Gini correlationpredictor importanceclassificationasymptotic normalitybootstrap testdependence measurecategorical response
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The pith

A test for the difference between two categorical Gini correlations enables comparison of predictor importance for categorical classification outcomes.

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

The paper develops an inferential method to compare how strongly different groups of numerical predictors relate to a categorical response variable. It builds on the categorical Gini correlation as a dependence measure and constructs a test statistic whose asymptotic distribution is normal under both the hypothesis of equal correlations and the hypothesis of differing correlations. The framework handles predictor groups that may have unequal numbers of variables and may be statistically dependent. A bootstrap procedure is also derived for inference, and the approach is illustrated with simulation studies plus applications to breast cancer and human activity recognition data.

Core claim

The central claim is that the difference of two categorical Gini correlations yields a test statistic that is asymptotically normal under both the null and alternative hypotheses, is consistent against alternatives, accommodates arbitrary and unequal predictor dimensions, and remains valid when the predictor groups are dependent.

What carries the argument

The difference of two categorical Gini correlations, together with the derived test statistic whose asymptotic normality is established under regularity conditions on the data.

If this is right

  • Predictor groups of arbitrary and unequal dimensions can be compared directly for their association with the categorical outcome.
  • The test remains valid when the two predictor groups exhibit dependence.
  • Inference can proceed either through the established asymptotic normal approximation or through a nonparametric bootstrap procedure.
  • The method supplies a practical tool for assessing relative predictor importance in classification problems with categorical responses.

Where Pith is reading between the lines

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

  • The framework could support sequential testing to rank more than two predictor groups in a single analysis.
  • Similar difference-of-dependence tests might be constructed for other categorical dependence measures beyond the Gini correlation.
  • In applied settings the test could guide feature-set selection before fitting a final classifier.

Load-bearing premise

The data distributions must satisfy regularity conditions that make the categorical Gini correlation a valid dependence measure and allow the central limit theorem to apply to the test statistic.

What would settle it

Large-sample simulations drawn from distributions that violate the regularity conditions should produce a test statistic whose empirical distribution deviates markedly from normality under the null hypothesis of equal correlations.

Figures

Figures reproduced from arXiv: 2605.17763 by Sameera Hewage, Yongli Sang.

Figure 1
Figure 1. Figure 1: Size and power of tests in Example 3.2(b). Dashed horizontal line is the nominal level 0.05. Example 3.3 (Binary Logistic Regression Model) In this example, we consider a logistic regression model where the binary response is generated as log  P(Z = 1|V ) P(Z = −1|V )  = −3 + 2V1 + 2V2 + 2V3 + 3 sin(V4) + 4V 2 5 , where V ∼ N(0, Σ) with Σ = (ρij )p×p having two scenarios ρij = 0 and ρij = 0.5 |j−i| , i ̸… view at source ↗
Figure 2
Figure 2. Figure 2: Top 15 Random Forest feature importances for the Wisconsin Breast Cancer dataset, [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
read the original abstract

This article proposes an inferential framework for comparing predictor importance in classification problems with categorical response variables. The approach is based on the categorical Gini correlation (CGC) proposed by Dang et al. (2020), a measure of dependence between numerical predictors and categorical outcomes. Predictor importance is evaluated by testing differences in CGCs across competing predictor groups. The proposed methodology accommodates predictors of arbitrary and unequal dimensions and allows for dependence between predictor groups. Asymptotic normality of the test statistic is established under both the null and alternative hypotheses, and the resulting test is shown to be consistent. In addition to deriving the asymptotic distribution, a nonparametric bootstrap procedure is developed as an alternative approach to inference. Simulation studies, along with applications to breast cancer and human activity recognition datasets, demonstrate the effectiveness of the proposed framework.

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 manuscript proposes a test for the difference between two categorical Gini correlations (CGCs) to compare predictor importance for a categorical response in classification settings. Extending Dang et al. (2020), it derives asymptotic normality of the difference estimator under both the null and alternative, proves consistency, accommodates unequal predictor dimensions, and allows dependence between the two predictor groups. A nonparametric bootstrap is also developed. The claims are supported by simulation studies and applications to breast cancer and human activity recognition data.

Significance. If the joint asymptotic results hold, the work supplies a practical inferential tool for assessing relative predictor strength when dimensions differ and groups may be dependent, which is common in classification. The bootstrap alternative and real-data examples add immediate usability. The extension to the difference of two CGCs under dependence fills a methodological gap left by the single-CGC theory in the cited prior work.

major comments (1)
  1. [§3.2, Theorem 3.1] §3.2, Theorem 3.1 and the subsequent joint CLT argument: the asymptotic normality claim under the alternative when the two predictor groups are dependent requires an explicit joint limiting distribution that incorporates the cross-covariance between the two empirical CGC estimators. The manuscript appears to state the marginal CLTs from Dang et al. (2020) and then invoke a delta-method step; without a displayed expression for the off-diagonal covariance term or a verification that the regularity conditions (e.g., finite moments of the joint kernel) remain sufficient under dependence, the limiting variance under HA is not fully secured.
minor comments (2)
  1. [§2.1] The notation for the two predictor vectors X and Y is introduced without an explicit statement that their dimensions p and q may be unequal; a short sentence clarifying this point would aid readability.
  2. [§4] Simulation tables report empirical rejection rates but do not include standard errors across the Monte Carlo replications; adding these would strengthen the evidence that the bootstrap and asymptotic versions behave comparably.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The point raised about the joint limiting distribution under dependence is well taken, and we address it directly below.

read point-by-point responses

  1. Referee: [§3.2, Theorem 3.1] §3.2, Theorem 3.1 and the subsequent joint CLT argument: the asymptotic normality claim under the alternative when the two predictor groups are dependent requires an explicit joint limiting distribution that incorporates the cross-covariance between the two empirical CGC estimators. The manuscript appears to state the marginal CLTs from Dang et al. (2020) and then invoke a delta-method step; without a displayed expression for the off-diagonal covariance term or a verification that the regularity conditions (e.g., finite moments of the joint kernel) remain sufficient under dependence, the limiting variance under HA is not fully secured.

    Authors: We agree that the presentation in Section 3.2 would benefit from an explicit statement of the joint limiting distribution of the two empirical CGC estimators under dependence. In the revision we will add the full asymptotic covariance matrix, including the off-diagonal cross-covariance term between the two U-statistic estimators, and apply the delta method to the difference. We will also verify that the moment conditions on the joint kernel (finite second moments) remain sufficient under the dependence structure permitted by the paper. These clarifications will be inserted into the statement of Theorem 3.1 and the surrounding text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines its test statistic from the categorical Gini correlation measure introduced in the independent prior work of Dang et al. (2020) and then derives the joint asymptotic normality of the difference under both null and alternative hypotheses, including the case of dependent predictor groups with unequal dimensions. This joint limiting distribution is presented as a new technical result rather than a direct renaming or algebraic reduction of the single-CGC asymptotics. The nonparametric bootstrap is offered as a separate computational alternative, not as the justification for the limiting distribution. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the derivation chain; the central claims therefore retain independent mathematical content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; therefore no specific free parameters, axioms, or invented entities can be extracted or audited from the provided text.

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