Stat 583

Advanced Theory of Statistical Inference


Administration
Evaluation
Assignments

Supplementary exercises


Content

Testing Statistical Hypotheses, Lehmann and Romano, 2005. (required text)
Mathematical Statistics, Shao, 2003. (supplemental text)

Course outline
  1. UMP Testing (LR Chapter 3)
    1. NP Lemma
    2. Montone likelihood ratio
  2. UMPU Testing (LR Chapters 4 and 5)
    1. One-parameter exponential families
    2. Similarity and completeness
    3. Multiparameter exponential families
    4. UMPU tests for normal models
  3. UMPI Testing (LR Chapters 6 and 7)
    1. Invariance
    2. Maximal invariants
    3. UMPI tests for normal models
  4. Bayesian Methods
    1. Confidence intervals
    2. BIC