Pursuing PhD with no relevant coursework. Is self study and publications sufficient to show competence?
Reading "stuff" doesn't demonstrate competency, but publishing papers certainly does. If you can "use" something, and demonstrate it, then no one will really question whether you are capable of using it. 

Don't worry about it, other than to worry about the difficulty of getting yourself to the point where publishers are willing to accept your papers. The rest will follow naturally. 

I'll point out that professionals do this as a matter of course. If they need competency in a subject to publish, then they just do it. They wouldn't normally take a course (for credit) and wouldn't require any certification. Academic life is, among other things, a continuous path of study.