Measure Theory and Asymptotic Statistics
DatesPeriod 1 - Aug 30, 2021 to Oct 22, 2021
- This is a crash course, highlighting the main principles of measure theory and asymptotic methods in statistics.
Sigma-algebras, measure, integration w.r.t. a measure, limit theorems, product measure and integration, change of measure, conditional expectation.
Multivariate central limit theorem, quadratic forms, delta-method, moment estimators, Z- and M-estimators, consistency and asymptotic normality, maximum likelihood estimators.
Solid knowledge of the principles of statistics and of mathematical analysis
Spreij, P.J.C. “Measure theoretic probability” Lecture notes (2018)
Van der Vaart, A.W. “Mathematische statistiek.” Lecture notes (1995): 1-77.