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A data-driven smooth test of symmetry

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  • Fang, Ying
  • Li, Qi
  • Wu, Ximing
  • Zhang, Daiqiang

Abstract

In this paper we propose a data driven smooth test of symmetry. We first transform the raw data via the probability integral transformation according to a symmetrized empirical distribution, and show that under the null hypothesis of symmetry, the transformed data has a limiting uniform distribution, reducing testing for symmetry to testing for uniformity. Employing Neyman’s smooth test of uniformity, we show that only odd-ordered orthogonal moments of the transformed data are required in constructing the test statistic. We present a standardized smooth test that is distribution-free asymptotically and derive the asymptotic behavior of the test and establish its consistency. Extension to dependent data case is discussed. We investigate the finite sample performance of the proposed tests on both homogeneous and mixed distributions (with unobserved heterogeneity). An empirical application on testing symmetry of wage adjustment process, based on heterogeneous wage contracts with different durations, is provided.

Suggested Citation

  • Fang, Ying & Li, Qi & Wu, Ximing & Zhang, Daiqiang, 2015. "A data-driven smooth test of symmetry," Journal of Econometrics, Elsevier, vol. 188(2), pages 490-501.
    • Handle: RePEc:eee:econom:v:188:y:2015:i:2:p:490-501
    DOI: 10.1016/j.jeconom.2015.03.013
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    Cited by:

    1. Dai, Xinjie & Niu, Cuizhen & Guo, Xu, 2018. "Testing for central symmetry and inference of the unknown center," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 15-31.
    2. Chen, Songnian & Zhou, Yahong & Ji, Yuanyuan, 2018. "Nonparametric identification and estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 202(2), pages 148-160.
    3. Sang, Yongli, 2024. "Test for diagonal symmetry in high dimension," Statistics & Probability Letters, Elsevier, vol. 205(C).
    4. Delgado, Miguel A. & Song, Xiaojun, 2018. "Nonparametric tests for conditional symmetry," Journal of Econometrics, Elsevier, vol. 206(2), pages 447-471.
    5. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    6. Niu, Cuizhen & Guo, Xu & Li, Yong & Zhu, Lixing, 2018. "Pairwise distance-based tests for conditional symmetry," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 145-162.

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