2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130560The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is given. The results developed in this paper have important applications to the theory of adaptation.Statistics Theory62G99 (Primary) 62F12, 62C20, 62M99. (Secondary)text