GRAPES Swedish Network for Graduate and Postgraduate Education in Statistics

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