Measure Theory and Asymptotic Statistics
DatesPeriod 1 - Aug 31, 2020 to Oct 23, 2020
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.
Spreij, P.J.C. “Measure theoretic probability” Lecture notes (2018)
Van der Vaart, A.W. “Mathematische statistiek.” Lecture notes (1995): 1-77.