Say you have in your hand a transition matrix published by Moody, and you also collected the rating information for a sample of bonds, which you use to form your own transition matrix. How can we use our sample to test whether if Moody's transition matrix is correct?
Depending upon how much data you have, you might find Violi (2004) useful.
Nickell et al. (2000), while principally considering time-dependent stability tests, refers a bit to significance testing between the matrices of different agencies and might also provide some insight.