**Lectures:** Tuesday, 4:30-7:10pm, Innovation Hall, room 133

The lectures will not be printed or posted on the web.

The required text is

The book has a few errata, mostly typos. (There were a few additional ones in the first printing, but I assume that by now most people will have the second printing or later.)

At the level of this course, no single text can cover "everything". The student is encouraged to study other texts on the various topics; see, for example, the references listed in the general description .

One learns mathematical theory primarily by individual work; that is, by supplying the successive steps in solving a problem or proving a theorem. Some mathematical theory is learned and reinforced by passive activities such as reading or listening to lectures and discussions, and the assigned readings and weekly lectures are meant to serve this purpose. The reading assignments listed in the schedule below should be carried out with a pencil and paper in hand. The readings should be iterated as necessary to achieve a complete understanding of the material.

The primary means of communication outside of class will be by email.

Students must use their Mason email accounts to receive important University information, including messages related to this class. (You may, of course, foward email from your Mason email account to one that you check regularly.)

If you send email to the instructor, please put "CSI 972" or "STAT 972" in the subject line.

Student work in the course (and the relative weighting of this work in the overall grade) will consist of

For in-class exams, one sheet of notes will be allowed. The preparation of that sheet is one of the most important learning activities.

The problems do not need to be worked sequentially (some are much harder than others); when you are stuck on one problem, go on to the next one.

Students are not to communicate concerning exams with each other or with any person other than
the instructor. On take-home exams, any **passive ** reference
is permissible (that is, the student
cannot ask someone for information, but the student may use any existing information from
whatever source).

Students are expected to read the relevant material in the text prior to each class (after the first one).

Students are strongly encouraged to solve the "exercises for practice and discussion", especially those marked with an asterisk.

- notation (mine and that in TPE2): vectors and matrices; standard spaces; functions; RVs; distributions (p.18 and p.25); etc.
- measure theory and integration
- probability theory
- special classes of probability distributions (group families and exponential families)
- statistics: sufficiency, anciliarity, minimality, completeness
- statistical decision theory; convex loss functions
- weak convergence

- statistics: sufficiency, anciliarity, minimality, completeness
- statistical decision theory; convex loss functions
- weak convergence

UMVUE

Nonparametric estimation; the information inequality

Equivariance (TPE2, Chapter 3):

First examples, location-scale families

Hand out midterm takehome.

Between now and the end of class on October 16, students are not to discuss homework or other aspects of the course (including the takehome of course!) with anyone other than the instructor.

Review inclass exam.

Equivariance (continuation of Chapter 3)

Minimaxity and admissibility (TPE2, Chapter 5).

Closed book and closed notes except for one sheet of prewritten notes.