Smoothed nonparametric tests and approximations of p-values

Yoshihiko Maesono, Taku Moriyama, Mengxin Lu

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)969-982
Number of pages14
JournalAnnals of the Institute of Statistical Mathematics
Issue number5
Publication statusPublished - Oct 1 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


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