Statistics 610a, Fall 2001
Texts and references

• I have only read a small part of Casella & Berger (2001), the text used in recent years. So far I am not greatly impressed.

• For general decision theory, Ferguson (1967) is still a good source. Hartigan (1983) is a good for elegant proofs, but it it written at a level far too advanced for this course.

• For topics such as the large-sample theory, I use Lehmann (1959, 1983) and Ibragimov & Hasminskii (1981). All three books are written at a slightly more demanding theoretical level than the Ferguson book.

• I will also draw ideas from other sources, including some of my own manuscripts. For exponential families I like Brown (1986). A few examples and problems will come from the primary literature. I will borrow examples from Bickel & Doksum (1977), which is the standard texts at many universities.

• For a quick overview, students might consult Silvey (1975). For penetrating discussions and meaty examples, Kiefer (1987) 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.

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

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

Casella, G. and Berger, R.L. (2001), Statistical Inference (Second Edition), Duxbury.

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

Gill & Levit (1995), Applications of the van Trees inequality: a Bayesian Cramér-Rao bound, Bernouilli 1, pp 59-79  

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

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

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

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

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

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.)