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Course

Measure Theory and Asymptotic Statistics


  • Teacher(s)
    Peter Spreij
  • Research field
    Econometrics
  • Dates
    Period 1 - Aug 29, 2022 to Oct 21, 2022
  • Course type
    Core
  • Program year
    First
  • Credits
    4

Course description

  • This is a crash course, highlighting the main principles of measure theory and asymptotic methods in statistics.
Topics covered:
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.

Prerequisites

Solid knowledge of the principles of statistics and of mathematical analysis

Course literature

Primary reading
Spreij, P.J.C. “Measure theoretic probability” Lecture notes (2018)
Van der Vaart, A.W. “Mathematische statistiek.” Lecture notes (1995): 1-77.