Holger Dette, Kathrin Möllenhoff, Dominik Wied
arXiv 6 Jun 2025 · Econometrics
arXiv:2506.06545 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Wied, D (2024) Semiparametric Distribution Regression with Instruments and Monotonicity self | 1.000 | 6 | 4 | 100% |
| 2 | Chernozhukov, V., I. Fernández-Val, and B. Melly (2013) Inference on Counterfactual Distributions | 0.737 | 5 | 3 | 40% |
| 3 | Foresi, S. and F. Peracchi (1995) The Conditional Distribution of Excess Returns: An Empirical Analysis | 0.737 | 3 | 2 | 100% |
| 4 | Chernozhukov, V., I. Fernández-Val, W. Newey, S. Stouli, and F. Vella (2020) Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models | 0.644 | 2 | 2 | 100% |
| 5 | Chernozhukov, V., I. Fernández-Val, and S. Luo (2025) +): Distribution Regression with Sample Selection and UK Wage Decomposition | 0.644 | 2 | 2 | 100% |
| 6 | Briseño-Sanchez, G., M. Hohberg, A. Groll, and T. Kneib (2020) Flexible Instrumental Variable Distributional Regression | 0.644 | 2 | 2 | 100% |
| 7 | Bradley, R. C (2007) Introduction to Strong Mixing Conditions. Vol 1-3 | 0.405 | 1 | 1 | 100% |
| 8 | Hörmann, S. and P. Kokoszka (2010) Weakly dependent functional data | 0.405 | 1 | 1 | 100% |
| 9 | Rothe, C. and D. Wied (2013) Misspecification Testing in a Class of Conditional Distributional Models | 0.405 | 1 | 1 | 100% |
| 10 | Wu, W. B (2005) Nonlinear system theory: Another look at dependence | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 30 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Synthetic Control Approach to Conditional Distributional Treatment Effects | 0.405 | 1 | 1 |