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Significance test for semiparametric conditional average treatment effects and other structural functions

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  • Zhou, Niwen
  • Guo, Xu
  • Zhu, Lixing

Abstract

The paper investigates a hypothesis testing problem concerning the potential additional contributions of other covariates to the structural function, given the known covariates. The structural function is the conditional expectation given covariates in which the response may depend on unknown nuisance functions. It includes classic regression functions and the conditional average treatment effects as illustrative instances. Based on Neyman's orthogonality condition, the proposed distance-based test exhibits the quasi-oracle property in the sense that the nuisance function asymptotically does not influence on the limiting distributions of the test statistic under both the null and alternatives. This novel test can effectively detect the local alternatives distinct from the null at the fastest possible rate in hypothesis testing. This is particularly noteworthy given the involvement of nonparametric estimation of the conditional expectation. Numerical studies are conducted to examine the performance of the test. In the real data analysis section, the proposed tests are applied to identify significantly explanatory covariates that are associated with AIDS treatment effects, yielding noteworthy insights.

Suggested Citation

  • Zhou, Niwen & Guo, Xu & Zhu, Lixing, 2024. "Significance test for semiparametric conditional average treatment effects and other structural functions," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:csdana:v:189:y:2024:i:c:s0167947323001500
    DOI: 10.1016/j.csda.2023.107839
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    References listed on IDEAS

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    1. Sokbae Lee & Ryo Okui & Yoon†Jae Whang, 2017. "Doubly robust uniform confidence band for the conditional average treatment effect function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1207-1225, November.
    2. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2008. "Nonparametric Tests for Treatment Effect Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 389-405, August.
    3. Minsu Chang & Sokbae Lee & Yoon‐Jae Whang, 2015. "Nonparametric tests of conditional treatment effects with an application to single‐sex schooling on academic achievements," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 307-346, October.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    5. Anne Leucht & Michael Neumann, 2013. "Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 349-386, April.
    6. Feng, Sanying & Kong, Kaidi & Kong, Yinfei & Li, Gaorong & Wang, Zhaoliang, 2022. "Statistical inference of heterogeneous treatment effect based on single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    7. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    8. Caiyun Fan & Wenbin Lu & Rui Song & Yong Zhou, 2017. "Concordance-assisted learning for estimating optimal individualized treatment regimes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1565-1582, November.
    9. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(4), pages 576-601, August.
    10. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    11. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    12. Shi, Chengchun & Song, R & Lu, W, 2021. "Concordance and value information criteria for optimal treatment decision," LSE Research Online Documents on Economics 102105, London School of Economics and Political Science, LSE Library.
    13. Leucht, Anne & Neumann, Michael H., 2009. "Consistency of general bootstrap methods for degenerate U-type and V-type statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1622-1633, September.
    14. Jason Abrevaya & Yu-Chin Hsu & Robert P. Lieli, 2015. "Estimating Conditional Average Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 485-505, October.
    15. Racine, Jeff, 1997. "Consistent Significance Testing for Nonparametric Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 369-378, July.
    16. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    17. Yu‐Chin Hsu, 2017. "Consistent tests for conditional treatment effects," Econometrics Journal, Royal Economic Society, vol. 20(1), pages 1-22, February.
    18. Qingyuan Zhao & Dylan S. Small & Ashkan Ertefaie, 2022. "Selective inference for effect modification via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 382-413, April.
    19. He, Yizeng & Kim, Soyoung & Kim, Mi-Ok & Saber, Wael & Ahn, Kwang Woo, 2021. "Optimal treatment regimes for competing risk data using doubly robust outcome weighted learning with bi-level variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    20. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
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