Title

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

DOI

https://doi.org/10.15672/HJMS.2015559562

Document Type

Article

Publication Date

1-1-2016

Publication Title

Hacettepe Journal of Mathematics and Statistics

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.

Volume

45

Issue

2

First Page

521

Last Page

540

Identifier

SCOPUS_ID:84964039901

Documento original

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