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The Wald–Wolfowitz runs test (or simply runs test), named after statisticians Abraham Wald and Jacob Wolfowitz is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data sequence. More precisely, it can be used to test the hypothesis that the elements of the sequence are mutually independent.
The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald [1] and later proven to be optimal by Wald and Jacob Wolfowitz. [2] Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem.
There are several reasons to prefer the likelihood ratio test or the Lagrange multiplier to the Wald test: [18] [19] [20] Non-invariance: As argued above, the Wald test is not invariant under reparametrization, while the likelihood ratio tests will give exactly the same answer whether we work with R, log R or any other monotonic transformation ...
Tukey–Duckworth test: tests equality of two distributions by using ranks. Wald–Wolfowitz runs test: tests whether the elements of a sequence are mutually independent/random. Wilcoxon signed-rank test: tests whether matched pair samples are drawn from populations with different mean ranks.
The Wald–Wolfowitz runs test tests for the number of bit transitions between 0 bits, and 1 bits, comparing the observed frequencies with expected frequency of a random bit sequence. Information entropy; Autocorrelation test; Kolmogorov–Smirnov test; Statistically distance based randomness test.
Abraham Wald (/ w ɔː l d /; Hungarian: Wald Ábrahám, Yiddish: אברהם וואַלד; () 31 October 1902 – () 13 December 1950) was a Jewish Hungarian mathematician who contributed to decision theory, [1] geometry and econometrics, and founded the field of sequential analysis. [2]
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Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American Jewish statistician and Shannon Award-winning information theorist. He was the father of former United States Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz .