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A device-independent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions concerning the quantum apparatus. Previous work mostly deals with the two-party version of this problem. In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment. Our dimension test stems from the study of a newarXiv:1707.03125v2 fatcat:xfmyvh5epnekzpyud5e76j4t3u