A data driven runs test to identify first order positive Markovian dependence

Year 2016, Volume: 45 Issue: 2, 521 - 540, 01.04.2016

Jimmy A. Corzo Myrian E. Vergara

Abstract

We propose a data driven test to identify first order positive Markovian
dependence in a Bernoulli sequence, based on a combination of two runs
tests: a well known runs test for the same purpose conditional on the
numbers of ones in the sequence, and a modified runs test independent
of the number of ones. We give analytic expressions for the exact
distribution of the modified runs test statistic and for its power; also
we built an algorithm to calculate it explicitly. To compare the power of
the tests, we calculated these for some values of the proportion of ones
and the success probability. We show that there are some intervals
for the success probability in which the new runs test surpasses the
power of the conditional test, and that the data driven test improves
the power of the two runs tests, when they are considered separately.

Keywords

Markov-dependent Bernoulli trials, Data driven runs test, Runs distributions, Hypothesis of randomness, Power of a test

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