The set theoretic approach to parameter estimation is introduced for the robust identification of the local subsystem parameters of an interconnected system. The main contribution of this paper is the introduction of a concept and method to estimate subsystem parameters in the presence of subsystem interactions and external disturbances. The subsystem parameter set estimation problem, from the input-output point of view, can be formulated as several parameter set estimation problems, each with ARMAX model structure. A two-step strategy is proposed to extend the optimal volume ellipsoid algorithm for parameter set estimation to ARMAX models. Simulation results are given to substantiate the theoretical development for subsystem parameter set estimation.