A Test Statistic for Weighted Runs

Abstract

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.

20 pages, 4 figures. Match published paper as close as possible

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