LIST of Most Important Topics Covered during Fall 2008
(in terms of Lecture Time, book coverage, and Exercises and Tests)
==================================================================

NB. During the Monday 12/15/08 review session, these topics 
will be annotated with specific Section and Subsection numbers
from the Bickel and Doksum and Rohatgi and Saleh texts.

TOPICS

(1) Statistical Models: identifiable parameters, ideas of
    coordinate changes of data and of parameters
    [Secs. 1.1.1-1.1.3]

(2) Sufficiency: definition, factorization theorem, 
    definition of completeness and minimal sufficient statistics, 
    proving minimality by showing that the log-likelihood 
    uniquely determines a particular sufficient statistic.
    Rao-Blackwellization.
    Finding UMVUE's based on complete sufficient statistics.
    [Sec. 1.5, 3.4.2 in Bickel-Doksum; Rohatgi & Saleh Sec. 8.3]

(3) Bayesian basics: defintions, posterior calculation, conjugate 
    priors.  [Sec.1.2]

(4) (Bayesian) Decision theory formulations of estimation and 
    hypothesis testing problems; randomized decision procedures; 
    relevance of posteriors to explicit solution for Bayes optimal
    decision rules in squared-error loss, absolute-error loss, and
    (weighted) misclassification-indicator loss problems.
    [Sec. 1.3, with additional explanation in Sec. 3.2]

(5) Estimating equations, Maximum Likelihood, Generalized Method of 
    Moment Estimation: definitions and calculation in simple examples.
    [Sec. 2.1, 2.2.2]

(6) Fisher Information & Cramer-Rao lower bound.
    Relation between Jensen inequality and bias.
    [Sec. 3.4.2, B.9.]

(7) Exponential families: recognizing and verifying
     --- identifiability of parameters
     --- rank of sufficient statistic;
    facts about natural canonical families 
     --- equivalence between identifiability & rank 
     conditions these and conditions based on A(eta),
     --- completeness of sufficient statistics for ;
    conjugate families of priors;
     --- MLE's as generalized moment estimators for 
     sufficient statistic;
     --- attainment of C-R bound by suff. stat. 
     [Sec. 1.6, 2.3, 3.4.2]

 (8) Neyman-Pearson Lemma & Likelihood ratio tests.
     Randomized & nonrandomized tests.
     Monotone Likelihood Ratio property and UMP tests.
     [Sec. 4.2 and 4.3.]


OTHER TOPICS [e.g. Delta Method, Multivariate Normal,
     Applying spectral representation of matrices &
     EM Algorithm ] which we covered will not be in 
     scope for the exam.


NOTES. You ought to be prepared to answer a short 
     question based on each definition and major theorem 
     in the list (1)-(8).