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Testing Conditional Stochastic Dominance at Target Points

Federico A. Bugni, Ivan A. Canay, Deborah Kim

arXiv 18 Mar 2025 · Econometrics

arXiv:2503.14747 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper introduces a novel test for conditional stochastic dominance (CSD) at specific values of the conditioning covariates, referred to as target points. The test is relevant for analyzing income inequality, evaluating treatment effects, and studying discrimination. We propose a Kolmogorov--Smirnov-type test statistic that utilizes induced order statistics from independent samples. Notably, the test features a data-independent critical value, eliminating the need for resampling techniques such as the bootstrap. Our approach avoids kernel smoothing and parametric assumptions, instead relying on a tuning parameter to select relevant observations. We establish the asymptotic properties of our test, showing that the induced order statistics converge to independent draws from the true conditional distributions and that the test is asymptotically of level $\alpha$ under weak regularity conditions. While our results apply to both continuous and discrete data, in the discrete case, the critical value only provides a valid upper bound. To address this, we propose a refined critical value that significantly enhances power, requiring only knowledge of the support size of the distributions. Additionally, we analyze the test's behavior in the limit experiment, demonstrating that it reduces to a problem analogous to testing unconditional stochastic dominance in finite samples. This framework allows us to prove the validity of permutation-based tests for stochastic dominance when the random variables are continuous. Monte Carlo simulations confirm the strong finite-sample performance of our method.

Citation extraction

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appendix boundary found by appendix_titled_section at “Extensions and Supplementary Analyses” · 79% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Goldman, M. and D. M. Kaplan (2018) Comparing distributions by multiple testing across quantiles or CDF values1.00064100%
2Shen, S. and X. Zhang (2016) Distributional Tests for Regression Discontinuity: Theory and Empirical Examples0.9285380%
3Hodges, J (1958) The significance probability of the Smirnov two-sample test0.87462100%
4McFadden, D (1989) Testing for stochastic dominance, in0.81142100%
5Bugni, F. A., I. A. Canay, and D. Kim (2025) On the Rate of Convergence of Induced Ordered Statistics and their Applications, Tech self0.7547343%
6Hajek, J., Z. Sidak, and P. K. Sen (1999) Theory of rank tests0.7373367%
7Blackman, J (1956) An extension of the Kolmogorov distribution0.64422100%
8Canay, I. A. and V. Kamat (2018) Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design self0.64422100%
9Durbin, J (1973) Distribution theory for tests based on the sample distribution function0.64422100%
10Gnedenko, B. V. and V. S. Korolyuk (1951) On the maximum divergence of two empirical distributions (in Russian)0.64422100%

Showing the top 10 of 42 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1On the Rates of Convergence of Induced Ordered Statistics and their Applications0.84333
2Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testing0.51121