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Smoothed nonparametric tests and approximations of p-values

Author

Listed:
  • Yoshihiko Maesono

    (Kyushu University)

  • Taku Moriyama

    (Kyushu University)

  • Mengxin Lu

    (Kyushu University)

Abstract

We propose new smoothed sign and Wilcoxon’s signed rank tests that are based on kernel estimators of the underlying distribution function of the data. We discuss the approximations of the p-values and asymptotic properties of these tests. The new smoothed tests are equivalent to the ordinary sign and Wilcoxon’s tests in the sense of Pitman’s asymptotic relative efficiency, and the differences between the ordinary and new tests converge to zero in probability. Under the null hypothesis, the main terms of the asymptotic expectations and variances of the tests do not depend on the underlying distribution. Although the smoothed tests are not distribution-free, making use of the specific kernel enables us to obtain the Edgeworth expansions, being free of the underlying distribution.

Suggested Citation

  • Yoshihiko Maesono & Taku Moriyama & Mengxin Lu, 2018. "Smoothed nonparametric tests and approximations of p-values," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 969-982, October.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:5:d:10.1007_s10463-017-0614-0
    DOI: 10.1007/s10463-017-0614-0
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    Cited by:

    1. Bagkavos, Dimitrios & Patil, Prakash N., 2021. "Improving the Wilcoxon signed rank test by a kernel smooth probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 171(C).

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