Abstract.
Starting with a sequence of i.i.d. [uniform] random variables with m possible values, we consider the overlapping Markov chain formed by sliding a window of size k through the i.i.d. sequence. We study the limiting covariance matrix B k of this Markov chain and give algorithms for constructing the eigenvectors of B k . We also discuss the applicability of the results in strengthening Pearson’s χ2 test as well as the relation to approximate entropy and the usefulness in the area of testing the hypothesis of uniformity of random number generators.
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Mathematics Subject Classification (2000): Primary: 60J10; Secondary: 11K45
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Alhakim, A. On the eigenvalues and eigenvectors of an overlapping Markov chain. Probab. Theory Relat. Fields 128, 589–605 (2004). https://doi.org/10.1007/s00440-003-0321-z
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DOI: https://doi.org/10.1007/s00440-003-0321-z
Keywords
- Finite Markov Chains
- Testing of Random Number Generators
- Limiting covariance matrix
- Chi-square statistic