Graduate student in or of?

I would say in Statistics.

The reason I say this is because you would say: I am majoring in Statistics.

Or in response to the question: What do you do for a living? You might say, "I'm in plastics."

You can say I'm a student of Statistics, and hence, it wouldn't be wrong to say graduate student of Statistics. But, I don't believe it is the common usage (in American English).

In Britain we do not 'major' in things.

As undergraduates we 'read' subjects. Even a chemist, spending 75% of their time in a laboratory, would be 'reading' chemistry.

At least that was always the case but younger people may well tell me I'm wrong.

For that reason I would say 'I am a post-graduate student of statistics'.

Only capitalize it if it's a major. AP would say no to this-- only if it's a language (French, English), but for your purposes it would be OK.

Otherwise, give your major first and then say you're specializing in statistics. Don't capitalize it.

I am an university student studying at Australia. Personally, i think you can say in this way:" I am a graduate student with major in statistics."