[ilzmastr]

You should state your goals and timeline. There is a lot of deep stuff that can be ignored by many... Often there is a good 1st book, another for 2nd, for 3rd, and hopefully not many more after that.

It also depends what community you ask, engineers vs mathematicians vs actual statisticians. So the community you want to be a part of is the one you should ask. It is probably too much of a melting pot here to get one of these flavors.

In my past I’ve looked at courses I wanted to take, and then looked at the chain of prerequisites and books used there, hws assigned, and did those. Nothing beats talking to the teachers who you think are good. Alternatively you could have colleagues who you like, and whose history you want to emulate.

Having a specific goal is important. Egregious amounts of time can be spent in many corners of probability theory and statistics. Especially in the case that steps are taken in the wrong order. Trying to do Billingsley without first taking real analysis would be crazy. And maybe studying from Billingsley is crazy for most people’s goals to begin with.

That said, I’ve enjoyed reading the suggestions here.