Parametric embedding of nonparametric inference problems

Mayer ALVO, Tze Leung LAI, Leung Ho Philip YU

Research output: Contribution to journalArticlespeer-review

1 Citation (Scopus)


In 1937, Neyman introduced the notion of smooth tests of the null hypothesis that the sample data come from a uniform distribution on the interval (0,1) against alternatives in a smooth parametric family. This idea can be used to embed various nonparametric inference problems in a parametric family. Focusing on nonparametric rank tests, we show how to derive traditional rank tests by applying this approach. We also show how to use it to obtain simplifying insights and optimality results in complicated settings that involve censored and truncated data, for which it is more convenient to use hazard functions to define the embedded family. We describe an application of the embedding approach to the problem of testing for trend in environmental studies. Copyright © 2018 Grace Scientific Publishing, LLC.
Original languageEnglish
Pages (from-to)151-164
JournalJournal of Statistical Theory and Practice
Issue number1
Early online dateDec 2017
Publication statusPublished - 2018


Alvo, M., Lai, T. L., & Yu, P. L. H. (2018). Parametric embedding of nonparametric inference problems. Journal of Statistical Theory and Practice, 12(1), 151-164. doi: 10.1080/15598608.2017.1399840


  • Parametric embedding
  • Nonparametric inference
  • Smooth tests
  • Censored and truncated data
  • Hazard rank tests


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