# Advanced Probability and Inference

## Content

- Mathematical background (limits, series, order relations and rates of convergence, continuity, sets)
- Measure theoretic foundations of probability (probability triplets, random variables, independence, expected values, change of variable)
- Stochastic convergence (almost sure convergence, convergence in probability, convergence in distribution, laws of large numbers, central limit theorems, non-iid stochastic variables)
- Conditional probability and expectation
- Statistical tests (size and critical values, power, efficiency, asymptotic tests, asymptotic relative efficiency)
- Estimation (confidence intervals, point estimation, asymptotic efficiency, Fisher Information)
- Nonparametrics (U-statistics, statistical functionals, limit distributions)

## Literature

Rosenthal, J.S., (2006), A First Look at Rigorous Probability Theory, 2nd ed., World Scientific.

Lehmann, E.L., (1999), Elements of Large Sample Theory, Springer.

Course page at Örebro University