Forget this whole dominance thing. I think it's a load of crap. Parrots bite out of fear, curiosity, territory, etc. They could also learn to bite for amusement or to be left alone. Learn what causes your parrot to bite and try to avoid that. Avoid putting it in situations where biting is more likely to occur. Create scenarios incompatible to biting (with a treat or toy in beak, biting is impossible). While we may try to punish out the last little bits of biting, the majority of it is definitely best dealt with using positive reinforcement of other behavior.
I will admit I've used the shake off method with Kili. But this was after extensive positive reinforcement training and virtually no biting. She never bit me for fear or distrust. Most of it was curious nipping (like trying to nip my ears or neck while on shoulder), so making it unworthwhile eliminated this last bit. But she was completely used to being on me and this punishment would make her avoid that behavior rather than being on me.
But now put yourself in the parrots shoes... "Come here so that I could punish you" is not exactly a good reason for it to come to you. If it is positive (and don't think treats are the only thing, fun toys/attention are also important), then the parrot will want to come to you. It has to know that you're not going to do things it doesn't want (or at least that the good outweighs the bad). You need to be smarter than the parrot. You need to purposefully shape your behavior and the environment that discourages biting and encourages positive interaction that makes the bird less fearful. Check out the articles on this site as they will give you a good starting point.








