Journal of Statistical Theory and Practice

, Volume 12, Issue 1, pp 151–164 | Cite as

Parametric embedding of nonparametric inference problems

  • Mayer Alvo
  • Tze Leung Lai
  • Philip L. H. YuEmail author


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.


Parametric embedding nonparametric inference smooth tests censored and truncated data hazard rank tests 

AMS Subject Classification



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Copyright information

© Grace Scientific Publishing 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  2. 2.Department of StatisticsStanford UniversityStanfordUSA
  3. 3.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongChina

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