On two statistics of chi-square type based on frequencies of tuples of states of a high-order Markov chain
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M. I. Tikhomirova
We consider a tuple of states of an (s – 1)-order Markov chain whose transition probabilities depend on a small part of s – 1 preceding states. We obtain limit distributions of certain χ2-statistics X and Y based on frequencies of tuples of states of the Markov chain. For the statistic X, frequencies of tuples of only those states are used on which the transition probabilities depend, and for the statistic Y, frequencies of s-tuples without gaps. The statistical test with statistic X which distinguishes the hypotheses H1 (a high-order Markov chain) and H0 (an independent equiprobable sequence) appears to be more powerful than the test with statistic Y . The statistic Z of the Neyman–Pearson test, as well as X, depends only on frequencies of tuples with gaps. The statistics X and Y are calculated without use of distribution parameters under the hypothesis H1, and their probabilities of errors of the first and second kinds depend only on the non-centrality parameter, which is a function of transition probabilities. Thus, for these statistics the hypothesis H1 can be considered as composite.
Copyright 2003, Walter de Gruyter
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- Independent systems of automata in labyrinths
- Estimation of the time needed to set up a covert channel
- Schemes of public distribution of keys based on a non-commutative group
- Characteristic polynomials of multi-index transportation problems
- Construction of maximally non-Hamiltonian graphs
- Generating triples of involutions of large sporadic groups
- On the number of reversible homogeneous structures
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- On two statistics of chi-square type based on frequencies of tuples of states of a high-order Markov chain
Articles in the same Issue
- Independent systems of automata in labyrinths
- Estimation of the time needed to set up a covert channel
- Schemes of public distribution of keys based on a non-commutative group
- Characteristic polynomials of multi-index transportation problems
- Construction of maximally non-Hamiltonian graphs
- Generating triples of involutions of large sporadic groups
- On the number of reversible homogeneous structures
- Random partitions of a set with given number of blocks
- On two statistics of chi-square type based on frequencies of tuples of states of a high-order Markov chain
