Reconstructing a Noisy Markov Chain Using Near-Neighbor Rules

Abstract

An observer desires to record a realization of a stationary two-state Markov chain X , but experimental conditions are such that he instead sees a realization of an error sequence Y . The objective is to reconstruct X . For a simple parameterization of both the Markov chain and the error sequence, a class of near-neighbor reconstruction rules is proposed and investigated. When the values of the parameters are unspecified, estimates are suggested and their asymptotic properties investigated. We are then able to calculate the large sample probability of using the best of the near-neighbor rules under consideration.