Title :
Universal Tests for Memory Words
Author :
Morvai, Gusztav ; Weiss, Benjamin
Author_Institution :
MTA-BME Stochastics Res. Group, Budapest, Hungary
Abstract :
The main result is a universal pointwise test that, when presented with a set of words S on a finite or countable alphabet X that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in S are memory words. For example, if S consists of all of the single letters in X, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given.
Keywords :
Markov processes; probability; Markov chain; countable alphabet X; finite alphabet X; memory words; positive probability words; stationary process; universal pointwise test; Frequency modulation; Indexes; Markov processes; Memory management; Probability distribution; Random variables; Time series analysis; Statistical learning; stationary processes; stochastic processes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2268913
