# Frequentist statistics references for someone well versed in modern probability theory

Coming from a rigorous background in analysis and modern probability theory, I find Bayesian statistics straightforward and easy to understand, and frequentist statistics incredibly confusing and unintuitive. It seems that frequentists are really doing bayesian statistics, except with "secret priors" that aren't well motivated or carefully defined.

On the other hand, a lot of great statisticians who understand both perspectives ascribe to the frequentist perspective, so there must be something there that I just don't understand. Rather than giving up and declaring myself a Bayesian, I'd like to learn more about the frequentist perspective to try to really "grok" it.

What are some good references for learning frequentist statistics from a rigorous perspective? Ideally I'm looking for definition-theorem-proof type books, or perhaps hard problem sets that, by solving them, I would gain the right mindset. I've read a lot of the more "philosophical stuff" one might find searching the internet - wiki pages, random pdfs from .edu/~randomprof sites, etc - and it hasn't helped.

• I was exactly like you ! Solid background in probability theory, but ignorant in statistics. And I was charmed by Bayesian statistics (especially Christian Robert's book). I learned frequentist statistics in Fourdrinier's book amazon.fr/… but I'm not sure you read French. Please let me note you're wrong about "secret priors". – Stéphane Laurent Sep 27 '12 at 7:10
• This is a very wide topic and it is important to understand the difference in the interpretation of the parameters. Given that you have a strong theoretical background, it will be easy for you to understand that, in the Bayesian paradigm, a parameter is a random variable while, in frequentist statistics, a parameter is a variable/number to be estimated. Therefore, there is nothing like frequentists are using "secret priors". You can find some references here. – user10525 Sep 27 '12 at 10:57

• @MichaelChernick Yes you're right I don't have a very good grasp of statistics, my goal is to remedy this. That frequentist idea is actually not intuitive to me at all.. :/ I was hoping if it is presented in full rigor with $\forall$'s and $\epsilon$'s and functions between sets and such, then I could make sense of it. Bayesian statistics is much easier since I can just think about conditional expectation of random variables. – Nick Alger Sep 30 '12 at 3:48