If my research is applying methods from field X to field Y, should I do my PhD in field X or field Y?

Let's say I'm a PhD student in a field, let's call it X, and my research is all based on taking the methods developed in field X and applying them to some other fields, let's call them Y, Z, and W. Let's further suppose that I do not make any contributions to the theory of X, I only apply it to Y, Z, and W. Is X the proper fit for me, or should I really pick my favorite of Y, Z, and W?