Libby,
Does this TV in fact have an in-built timer? I was unable to find a User Manual on the 'net, but the few reviews I found didn't mention a timer feature. What does the owner's manual say about a timer?
You didn't give us any history of the problem. Have you just acquired the set? Brand new or second-hand? Did it do this from the beginning, or has it only recently started switching on at 3am?
If it doesn't have a timer, my suspicion would shift to a poorly-designed standby circuit that's being triggered by a voltage spike on the mains power, causing it to come out of standby when it shouldn't. Is there any other electric appliance in your house that switches on at 3am - maybe an air-con, off-peak hot water system, dishwasher, etc?
Daniel