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AMS 571, Mathematical Statistics
Sampling distribution; convergence concepts; classes of statistical models; sufficient statistics; likelihood principle; point estimation; Bayes estimators; consistency; Neyman-Pearson Lemma; UMP tests; UMPU tests; Likelihood ratio tests; large sample theory. 
PrerequisiteAMS 570 preferred but not required
3 credits, ABCF grading 

Text: "Statistical Inference" by George Casella and Roger L. Berger, 2nd edition; Duxbury Advanced Series, 2002;
ISBN: 978-0-534-24312-8 

Fall Semester

Learning Outcomes:

1) Demonstrate deep understanding of mathematical concepts on statistical methods in:
      * Sampling and large-sample theory;
      * Sufficient, ancillary and complete statistics;
      * Point estimation;
      * Hypothesis testing;
      * Confidence interval.

2) Demonstrate deep understanding in advanced statistical methods including:
      * Maximum likelihood, method of moment and Bayesian methods;
      * Evaluation of point estimators, mean squared error and best unbiased estimator;
      * Evaluation of statistical tests, power function and uniformly most powerful test;
      * Interval estimation based on pivot quantity or inverting a test statistic.

3) Demonstrate skills with solution methods for theoretical proofs:
      * Almost sure convergence, convergence in probability and convergence in distribution;
      * Ability to follow, construct, and write mathematical/statistical proofs;
      * Ability to derive theoretical formulas for statistical inference in real-world problems.

4) Develop proper skillsets to conduct statistical research:
      * Ability to understand and write statistical journal papers; 
      * Ability to develop and evaluate new statistical methods;
      * Ability to adopt proper statistical theories in research.

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