Statistical Aspects of Lumpability Hypotheses for Markov Chains.
Marlin U. Thomas, Donald R. Barr · Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School) · 1973
Under certain conditions the state space of a discrete parameter Markov Chain may be partitioned to form a smaller lumped chain that retains the Markov property. The problem of formulating lumpability hypotheses when the transition probability matrix P is not known and, hence, must be estimated is discussed. An approximate test of these hypotheses is described based on well known non-parametric methods. The procedure is illustrated by an example. (Author)