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Practically significant differences between conditional distribution functions

Holger Dette, Kathrin Möllenhoff, Dominik Wied

arXiv 6 Jun 2025 · Econometrics

arXiv:2506.06545 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null) hypothesis that the $L^2$ distance between the conditional distribution functions does not exceed a certain threshold in absolute value. The consideration of these hypotheses is motivated by the observation that in applications, it is rare, and perhaps impossible, that a null hypothesis of exact equality is satisfied and that the real question of interest is to detect a practically significant deviation between the two conditional distribution functions. The consideration of a composite null hypothesis makes the testing problem challenging, and in this paper we develop a pivotal test for such hypotheses. Our approach is based on self-normalization and therefore requires neither the estimation of (complicated) variances nor bootstrap approximations. We derive the asymptotic limit distribution of the (appropriately normalized) test statistic and show consistency under local alternatives. A simulation study and an application to German SOEP data reveal the usefulness of the method.

Citation extraction

30
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44
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distinct cited
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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
1Wied, D (2024) Semiparametric Distribution Regression with Instruments and Monotonicity self1.00064100%
2Chernozhukov, V., I. Fernández-Val, and B. Melly (2013) Inference on Counterfactual Distributions0.7375340%
3Foresi, S. and F. Peracchi (1995) The Conditional Distribution of Excess Returns: An Empirical Analysis0.73732100%
4Chernozhukov, V., I. Fernández-Val, W. Newey, S. Stouli, and F. Vella (2020) Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models0.64422100%
5Chernozhukov, V., I. Fernández-Val, and S. Luo (2025) +): Distribution Regression with Sample Selection and UK Wage Decomposition0.64422100%
6Briseño-Sanchez, G., M. Hohberg, A. Groll, and T. Kneib (2020) Flexible Instrumental Variable Distributional Regression0.64422100%
7Bradley, R. C (2007) Introduction to Strong Mixing Conditions. Vol 1-30.40511100%
8Hörmann, S. and P. Kokoszka (2010) Weakly dependent functional data0.40511100%
9Rothe, C. and D. Wied (2013) Misspecification Testing in a Class of Conditional Distributional Models0.40511100%
10Wu, W. B (2005) Nonlinear system theory: Another look at dependence0.40511100%

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Cited by, within the corpus

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

Citing paperIntensityMentionsSections
1A Synthetic Control Approach to Conditional Distributional Treatment Effects0.40511