Did the ghost really murder his wife? If yes, then why?

The Canterville ghost did really kill his wife. When the sweet Virginia asks him about it, he says:

 'Well, I quite admit it,' said the ghost, 'but my wife was not very nice, you know, and she knew nothing about cookery. However, it is all over now, and I don't think it was very nice of her brothers to starve me to death.'

This, on the surface, is a light hearted story with Wilde's characteristic comic touch. The ghost killed his wife because she didn't know how to cook. At first, we might laugh. 

However, Wilde really doesn't make light of this murder. We learn right away that the ghost had to pay a price: her brothers starved him to death. But then he pays a steeper price, for he must wander forever as a ghost, not alive, but not dead, somewhere between human and inhuman, unless someone innocent and pure redeems him. He can never get rid of his guilt, never be at peace, until he can die. We know that he is guilty--that killing his wife is not a joke--because of his desperate desire to be at rest.