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.)