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) 

Schedule

Jan 24, 13-16, P258
Jan 25, 9-12, L111

Jan 31, 9-12, G102
Feb 1, 13-16, L111

Feb 21, 9-12, P138
Feb 22, 13-16, P221

March 6, 9-12, P254
March 7, 13-16, P243

March 20, 9-12, P243
March 21, 13-16, L151

Course Data
University: 
Örebro
Type of schedule: 
Travel friendly schedule
Level: 
PhD
Credits (ECTS): 
12.00
Offered: 
2012:1