General aviation pilot reported a NMAC during approach with an aircraft not communicating on UNICOM.

Narrative

Upon completing the hold at SOITE for the ILS 6 at MJX; my ADSB showed a plane approaching me from behind at approximately 500ft MSL above. While continuing my approach on ILS 6; waiting for glideslope intercept; the aircraft was gaining on me. I then began a slow decent to increase the vertical distance; but ADSB still showed 500ft; I assume he was descending also. By this point I made several calls over UNICOM to announce that I was on the ILS 6 at MJX on 122.800. I never heard any calls or response from this aircraft of his intentions or acknowledgment. I then observed him overtake my aircraft 500ft directly above me on the approach; I continued my approach to the ILS 6 as he also continued towards runway 6 at MJX with radio silence. I attempted 3 times to reach him on the radio but received no response from that aircraft.There were several planes in the pattern at MJX; and I proceeded to reach out to caution them on UNICOM about the plane on final not talking on frequency. I observed him maneuver to a low approach over runway 6 and proceed to exit the pattern northbound back to ZZZ. This aircraft was not on frequency the whole time and made no attempt to maneuver around me before or after the close miss. This pilot demonstrated unsafe airmanship and put my life and those in the traffic pattern at risk.