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A Central Limit Theorem for Non-Overlapping Return Times

  • Oliver Johnson (a1)

Abstract

Define the non-overlapping return time of a block of a random process to be the number of blocks that pass by before the block in question reappears. We prove a central limit theorem based on these return times. This result has applications to entropy estimation, and to the problem of determining if digits have come from an independent, equidistributed sequence. In the case of an equidistributed sequence, we use an argument based on negative association to prove convergence under conditions weaker than those required in the general case.

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Copyright

Corresponding author

Postal address: Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK. Email address: otj1000@cam.ac.uk

References

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A Central Limit Theorem for Non-Overlapping Return Times

  • Oliver Johnson (a1)

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