Parametric embedding of nonparametric inference problems

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....

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Bibliographic Details
Published in:Journal of statistical theory and practice 2018-01, Vol.12 (1), p.151-164
Main Authors: Alvo, Mayer, Lai, Tze Leung, Yu, Philip L. H.
Format: Article
Language:English
Subjects:
62G
censored and truncated data
hazard rank tests
nonparametric inference
Parametric embedding
Probability Theory and Stochastic Processes
smooth tests
Statistical Theory and Methods
Statistics
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Summary: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.
ISSN:1559-8608
1559-8616
DOI:10.1080/15598608.2017.1399840