Texts: required Peter Bickel and Kjell Doksum, Mathematical
Statistics, vol.I, 2nd ed., Pearson Prentice Hall, 2007.
(recommended)
V. Rohatgi and A.K. Saleh, An Introduction to Probability and Statistics,
2nd ed., Wiley.
I. Remaining topics in Testing & Confidence Regions
A. Unbiased Tests, Locally Most Powerful Tests, (Generalized)
Likelihood Ratio Tests
(Rohatgi & Saleh 9.5, 9.6, 10.2; Bickel and Doksum Sec. 4.9)
B. Pivots, Confidence Regions, Duality between Testing and
Confidence Sets, Uniformly Most Accurate Confidence Sets
(Rohatgi & Saleh 11.1-11.3; Bickel and Doksum 4.4-4.6)
C. Prediction Intervals, Bayesian Credible Sets and Predictive
Distributions
(Bickel and Doksum 4.7-4.8)
II. Asymptotic Estimation Theory, part 1
A. Large sample behavior of Method of Moments Estimators,
application to MLE's in Exponential Families
(Bickel & Doksum Ch. 5 through Sec 5.3)
B. Large sample behavior of one-dimensional MLE's and related
(Min Contrast and M) estimators
(Bickel & Doksum Ch. 5 Sec 5.4)
III. Asymptotic Estimation Theory, part 2
A. Multidimensional asymptotic theory for MLE and reslted estimators
(Bickel & Doksum Ch. 6 Sections 1 and 2)
IV. Large Sample (Multivariate) Methods
A. Large Sample Tests and Confidence Regions, based on Likelihood
Ratios, Wald Tests, and Score Statistics
(Bickel & Doksum Ch. 6 Sec.3)
B. Large Sample Tests for Discrete Data: Multinomial goodness of
fit and Logistic Regression
(Bickel & Doksum Ch. 6 Sec.4)
V. Nonparametrics, Rohatgi & Saleh Ch. 13