Perhaps I wasn't very clear: I was referring to
locally mandated specific exceptions to the general rule (valid not just in USA but all over the world), which is to never deviate from your ATC clearance unless in an emergency or a TCAS RA! Deciding to establish on a localizer from a radar vector without being cleared to do so would constitute deviating from a clearance.
I realize the first poster was referring to LAX, just pointing out that at some major ports around the world an autonomous turn to final is not an unheard-of procedure, and is in fact mandatory.