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A Unified Nonparametric Test of Transformations on Distribution Functions with Nuisance Parameters

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  • Xingyu Li
  • Xiaojun Song
  • Zhenting Sun

Abstract

This paper proposes a simple unified approach to testing transformations on cumulative distribution functions (CDFs) in the presence of nuisance parameters. The proposed test is constructed based on a new characterization that avoids the estimation of nuisance parameters. The critical values are obtained through a numerical bootstrap method which can easily be implemented in practice. Under suitable conditions, the proposed test is shown to be asymptotically size controlled and consistent. The local power property of the test is established. Finally, Monte Carlo simulations and an empirical study show that the test performs well on finite samples.

Suggested Citation

  • Xingyu Li & Xiaojun Song & Zhenting Sun, 2022. "A Unified Nonparametric Test of Transformations on Distribution Functions with Nuisance Parameters," Papers 2202.11031, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:2202.11031
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    References listed on IDEAS

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    1. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    2. Qihui Chen & Zheng Fang, 2019. "Inference on Functionals under First Order Degeneracy," Papers 1901.04861, arXiv.org.
    3. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
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    Cited by:

    1. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    2. Jiang, Hongyi & Sun, Zhenting & Hu, Shiyun, 2024. "A nonparametric test of mth-degree inverse stochastic dominance," Economics Letters, Elsevier, vol. 244(C).

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