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One- and two-sample nonparametric tests for the signal-to-noise ratio based on record statistics

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  • Damien Challet

Abstract

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and Wilcoxon signed-rank statistics as long as the data are not too heavy-tailed. Three two-sample parametric r-statistics are proposed, one with a higher specificity but a smaller sensitivity than Mann-Whitney U-test and the other one a higher sensitivity but a smaller specificity. A nonparametric two-sample r-statistic is introduced, whose power is very close to that of Welch statistic for Gaussian or uniformly distributed variables.

Suggested Citation

  • Damien Challet, 2015. "One- and two-sample nonparametric tests for the signal-to-noise ratio based on record statistics," Papers 1502.05367, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1502.05367
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    Cited by:

    1. Damien Challet, 2017. "Sharper asset ranking from total drawdown durations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(1), pages 1-22, January.

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