Counting the number of local extrema of the cumulative sum of data points yields the R-test, a new single-sample non-parametric test. Numeric simulations indicate that the R-test is more powerful than Student's t-test for semi-heavy and heavy-tailed distributions, equivalent for Gaussian variables and slightly worse for uniformly distributed variables . Finally the R-test has a greater power than the single-sample Wilcoxon signed-rank test in most cases .
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 .
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Counting the number
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records
D
local extrema of
R
data points yields the R-test, a new
the sample. The
R
non-parametric test. Numeric simulations indicate that the R-test is more powerful than
r-statistic is almost as powerful as
R
t-test for semi-heavy
t-statistic for Gaussian
D
heavy-tailed distributions, equivalent for Gaussian variables and slightly worse for
R
. Finally the R-test has a greater power than the single-sample
, and more powerful than the sign and
R
test in most cases
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