Statistics 610a, Fall 2001
A systematic development of the mathematical theory of statistical
inference covering methods of estimation, hypothesis testing, and
confidence intervals. An introduction to statistical decision
theory. Undergraduate probability at the level of Statistics 241a
|Office hours:||Wednesday 3:00 - 4:00, or by appointment
|Time:||Monday, Wednesday 1:00 - 2:20
Aim of the course
I hope that students who complete the course will be able to read some
of the current statistical or econometrics literature, or at least understand the
the standard theory behind those literatures. The course covers a range of topics
Statistics 242 (with the exception of
the theory of linear models, which is covered in
but the treatment will be more rigorous.
In particular, the course will put more emphasis on the decision-theoretic
interpretation of statistical procedures.
An understanding of statistical theory at the level of this course is
necessary background for many of the more advanced courses offered by the
As with all my graduate courses, there will be no exams. The final grade will
be based completely on the homework assignments. I expect to hand out about
ten assignments during the course. Details of my grading system will be
explained in the first class.
Texts and references
In the past I have worked from a number of books, none of which I have found
completely satisfactory. For the current course, I intend to borrow from several sources,
as described in the reference list.
For some topics, I will provide notes specifically written for this class.
- Statistical models as truth and approximation
- Principles and philosophies:
- information inequality (including the van Trees inequality)
- Neyman-Pearson approach to testing and confidence intervals
- decision theoretic framework: loss and risk functions; admissibility; minimax; quadratic loss
- large sample approximations
- M-estimation and maximum likelihood
- likelihood ratio theory
- efficiency: Fisherian and modern approaches