- You are here:
- Home
Department:
MATH
Course Number:
6262
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every spring semester
Basic theories of statistical estimation, including optimal estimation in finite samples and asymptotically optimal estimation. A careful mathematical treatment of the primary techniques of estimation utilized by statisticians.
Course Text:
At the level of Lehmann, Theory of Point Estimation
Topic Outline:
- Statistical decision theory: geometry of decision problems, the fundamental theorem of game theory and its use in statistical decision theory, specialized techniques for finding minimax and Bayes estimators in standard problems of estimation
- The Bayesian viewpoint: solving the no-data problem and using it in univariate and multivariate settings, detailed analysis for conjugate priors
- Optimality under restrictions:
- Minimum variance unbiased estimation: the Rao-Blackwell and Lehmann-Scheffe theorems
- Equivariant estimation: invariance of statistical problems under groups and some applications in estimation
- Asymptotic theory of estimation:
- General notions of asymptotic optimality: Hodges counterexample
- Le-Cam's theorem on asymptotic optimality
- Asymptotic optimality of maximum likelihood estimators, special cases including logistic regression
- Robust estimators (M, L, and R) and their asymptotic relative efficiencies
- Asymptotic optimality of Bayes estimators including higher order analysis characterizing asymptotic posterior distributions