Statistics 610a

Fall 1995

* An understanding of statistical theory at the level of this course is
necessary background for many of the more advanced courses offered by the
Statistics Department.*

As Ferguson has explained in his preface, a number of topics do not fit comfortably into a decision-theoretic interpretation. Nevertheless, some of those topics are vital for an understanding of modern statistics. I will supplement Ferguson's treatment with material on large-sample theory (in particular, maximum likelihood estimation, and likelihood ratio theory).

Students should not be intimidated by the references to Lebesgue integration in the early parts of the Ferguson book. I will take pains to keep the treatment accessible to anyone who understands the probability theory treated in Statistics 241a.

I will also draw ideas from other sources, including some of my own manuscripts. For exponential families I like {Brown86book}. A few examples and problems will come from the primary literature. I will borrow examples from {BickelDoksum77book}, which is the standard texts at many universities.

For a quick overview, students might consult {Silvey75book}. For penetrating discussions and meaty examples, {Kiefer87book} is good, in places. I have used both books on several occasions as the text for the course. Unfortunately neither book seemed popular with the classes.

{BickelDoksum77book}

Bickel, P. J. & Doksum, K. A. (1977), * Mathematical Statistics: Basic
Ideas and Selected Topics*, Holden-Day, San Francisco.

{Brown86book}

Brown, L. D. (1986), * Fundamentals of Statistical Exponential Families*,
Institute of Mathematical Statistics, Hayward, California.

{Ferguson67book}

Ferguson, T. S. (1967), * Mathematical Statistics: A Decision Theoretic
Approach*, Academic Press, Boston.

{Hartigan83book}

Hartigan, J. A. (1983), * Bayes Theory*, Springer, New York.

{IbragimovHasminskii81book}

Ibragimov, I. A. & Has'minskii, R. Z. (1981), * Statistical Estimation:
Asymptotic Theory*, Springer, New York.

{Kiefer87book}

Kiefer, J. C. (1987), * Introduction to Statistical Inference*,
Springer-Verlag, New York.

{Lehmann59TSH}

Lehmann, E. L. (1959), * Testing Statistical Hypotheses*, Wiley, New York.
(Later edition published by Chapman and Hall.)

{Lehmann83TPE}

Lehmann, E. L. (1983), * Theory of Point Estimation*, Wiley, New York.
(Later edition published by Chapman and Hall.)

{Silvey75book}

Silvey, S. D. (1975), * Statistical Inference*, Vol. 7 of * Monographs
on Statistics and Applied Probability*, Chapman and Hall, London.
(Originally published by Penguin Books. Republished at some time in
the 1990's by Chapman and Hall. ISBN 0-412-13820-4.)