What criteria does ATC apply to determine if an aircraft is established on the localizer if the pilot does not report it?
Each instrument approach consists of a lateral part and a vertical part, in the case of the ILS approach these are: localizer and glideslope. 

Aircraft are usually vectored to intercept the localizer approximately 1-2nm before the Final Approach Fix (FAF), where the glideslope is captured. Aircraft can be vectored onto the localizer as far as 20-25nm out, depending on terrain, localizer equipment and many other factors. If an aircraft is not established on the localizer, there is no point in continuing the approach, so it will be cancelled and the aircraft revectored.

If the aircraft is established on the localizer, it will try to intercept the glideslope, which is the vertical guidance system in the ILS approach. For VOR/DME, LOC/DME, NDB/DME or RNAV approaches, the vertical guidance is either achieved through correlation of location to a specific altitude in the chart or technical means which do not require a glideslope.

If an aircraft passes the Final Approach Fix and does not seem to descend, it will be considered as not established and the approach clearance will be cancelled, instructing the aircraft to either follow the missed approach procedure or manually vectoring the aircraft for another approach.