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.
Required Textbook: Statistical Inference by George Casella and Roger L. Berger, 2nd edition, 2002, Duxbury Advanced Series
Supplementary Textbooks:
- Introduction to Mathematical Statistics by Robert Hogg, Joseph McKean and Allen Craig, 8th edition, 2018, Pearson
- Mathematical Statistics and Data Analysis by John A. Rice, 3rd edition, 2006, Cengage
- Introduction to Mathematical Statistics and Its Applications by Richard Larsen and Morris Marx, 6th edition, 2017, Pearson
- John E. Freund’s Mathematical Statistics with Applications by Irwin Miller and Marylees Miller, 8th edition, 2018, Pearson
Learning Outcomes
- Understand mathematical concepts on statistical methods in:
- Probability and distributions;
- Sampling;
- Estimation;
- Hypothesis testing.
- 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.
- 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.
- Demonstrate the ability to follow, construct, and write mathematical proofs.
- Demonstrate understanding of how statistics is used in the solution of real-world problems.
- Demonstrate understanding of the assumptions, derivation of formulae, interpretation of results from statistical analysis.
- Understand the meaning of the statistical theorems and formulas, and the implication of it in real problems.
- Gain the ability to develop theories for statistical inference and testing for research on real-world problems.