On two–block–factor sequences and one–dependence

Abstract:

The distributions of two–block–factors $(f (\eta _{i},\eta _{i+1}); i \geq 1)$ arising from i.i.d. sequences $(\eta _{i}; i \geq 1)$ are observed to coincide with the distributions of the superdiagonals $(\zeta _{i,i+1}; i \geq 1)$ of jointly exchangeable and dissociated arrays $(\zeta _{i,j}; i, j \geq 1)$. An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one–dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two–block factor.