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A Central Limit Theorem for Non-Overlapping Return Times

Part of: Multivariate analysis Communication, information Limit theorems

Published online by Cambridge University Press:  14 July 2016

Oliver Johnson
Oliver Johnson*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK. Email address: otj1000@cam.ac.uk
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Abstract

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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.

Keywords

Central limit theorementropy estimationmatch lengthnegative associationreturn time

MSC classification

Primary: 94A17: Measures of information, entropy
Secondary: 60F05: Central limit and other weak theorems 62H20: Measures of association (correlation, canonical correlation, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 32 - 47
Copyright
© Applied Probability Trust 2006 

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