A Test Statistic for Weighted Runs

Details A Test Statistic for Weighted Runs A Test Statistic for Weighted Runs

2010-05-18

arxiv.org/abs/1005.3233v2

Mathematics

Statistics Theory

19 pages, 4 figures. Added new section on power of the test statistic

Scientific paper

A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the ordering of observations and provides additional sensitivity to local deviations from expectations. The exact distribution of the statistic in the non-parametric case is derived and an algorithm to compute $p$-values is presented. The computational complexity of the algorithm is derived employing a novel identity for integer partitions.

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