AMS 570, Introduction to Mathematical Statistics

Probability and distributions; multivariate distributions; distributions of functions of random variables; sampling distributions; limiting distributions; point estimation; confidence intervals; sufficient statistics; Bayesian estimation; maximum likelihood estimation; statistical tests.

Prerequisite: AMS 507

Spring, 3 credits, ABCF grading

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

 

Learning Outcomes:

1) Understand mathematical concepts on statistical methods in:
       * Probability and distributions;
       * Sampling;
       * Estimation;
       * Hypothesis testing.

2) Demonstrate skills with solutions for basic statistical methods including:
        * Expectation, variance and moment generating functions for various distributions;
        * Consistency and Limiting distributions;
        * Baysian methods;
        * Maximum likelihood methods, method of moments, empirical methods, random number generation, and other techniques.

3) Understand mathematical properties of methods used in statistics:
      * Apply knowledge derived from the mathematical subjects including calculus, analysis, and linear algebra;
      * Provide a derivation for statistical formulas.

4) Demonstrate the ability to follow, construct, and write mathematical proofs.

5) Demonstrate understanding of how statistics is used in the solution of real-world problems.

6) Demonstrate understanding of the assumptions, derivation of formulae, interpretation of results from statistical analysis.

7) Understand the meaning of the statistical theorems and formulas, and the implication of it in real problems.

8) Gain the ability to develop theories for statistical inference and testing for research on real-world problems.