>>10348837actual statistical theory has a lot of vocabulary you have to get used to, and is not as neatly packaged as fields like analysis and algebra. If you have a background in probability it should be easy enough to get used to but if you don't then you need to start from the basics and get familiar with the notation and vocabulary at a basic level. The following is a good sequence of topics:
1. Probability review: random variables, discrete and continuous distributions, densities, transformations of random variables and confidence intervals (as random intervals), characteristic functions. Theory of estimation of parameters, bias, MSE etc.
2. Formal hypothesis testing: intro to Neyman-Pearson framework, Neyman-Pearson's lemma on simple hypothesis testing, type I/II errors, power analysis, basic examples including hypotheses with the binomial distribution and the normal distribution (t-test, z-test), look into generalizations of the lemma in connection with UMPUs
3. Further hypothesis testing (skip if not relevant): More tests, non-parametric alternatives, ANOVA etc. the basic arsenal of any general science student
4. Further probability: Here is where the bulk of the theory is, learn about different modes of convergence: start only with convergence in probability and convergence in distribution and their relationships. Law of large numbers, Slutsky's theorem, central limit theorems and continuous mapping theorems. Apply this in the context of estimation, find consistent estimators etc.
5. Further estimation: Continue from (4), learn more kinds of properties of estimators. Fisher information and especially its relationship with UMVU and Cramer-Rao's bound
6. Linear models: Lots of theory that I forgot about but its just lots of linear algebra, but practical application is somewhat easy
