18.655
Mathematical Statistics
Decision theory, estimation, confidence intervals, hypothesis testing. Introduces large sample theory. Asymptotic efficiency of estimates. Exponential families. Sequential analysis. Prior exposure to both probability and statistics at the university level is assumed.
Spring 2016
Topics
- Course Overview
- Statistical Models
- Bayesian Models
- Decision Theoretic Framework
- Prediction
- Sufficiency
- Exponential Families I
- Exponential Families II
- Methods of Estimation I
- Methods of Estimation II
- Bayes Procedures
- Minimax Procedures
- Unbiased Estimation and Risk Inequalities
- Convergence of Random Variables Probability Inequalities
- Limit Theorems
- Asymptotics I: Consistency and Delta Method
- Asymptotics II: Limiting Distributions
- Asymptotics III: Bayes Inference and Large-Sample Tests
- Gaussian Linear Models
- Generalized Linear Models
- Case Study: Applying Generalized Linear Models
Readings
- Berger, J. Statistical Decision Theory and Bayesian Analysis (Springer Series in Statistics) . 2nd edition. Springer, 1993. ISBN: 9783540960980.
- Ferguson, T. J. Mathematical Statistics: A Decision Theoretic Approach . Academic Press, 1967. ISBN: 9781483207803.
- Lehmann, E. L. Testing Statistical Hypotheses . John Wiley & Sons Inc., 1986. ISBN: 9780471840831.
- Lehmann, E. L., and J. P. Romano. Testing Statistical Hypotheses . 3rd edition. Springer, 2008. ISBN: 9780387988641.
- Lehmann, E. L. Theory of Point Estimation . John Wiley & Sons Inc., 1983. ISBN: 9780471058496.
- Lehmann, E. L., and G. Casella. Theory of Point Estimation . 2nd edition. Springer, 2003. ISBN: 9780387985022.
Prerequisites & course information
Prereq: ( 18.650[J] and ( 18.100A , 18.100A , 18.100P , or 18.100Q )) or permission of instructor G (Spring) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Spring 2016
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.