In one representative embodiment, a prosthetic valve assembly comprises a valve component comprising a radially compressible and expandable frame and a valve structure supported inside of the frame. The valve structure is configured to allow blood to flow through the valve component in one direction and block the flow of blood in the opposite direction. The assembly further comprises a radially compressible and expandable anchor comprising an annular base and a plurality of cantilevered fixation members extending from the base. The fixation members are configured to pivot inwardly toward the valve component when the valve component is radially expanded within the anchor.