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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.
Prerequisite: AMS 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;
1) Demonstrate deep understanding of mathematical concepts on statistical methods
* 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.