STAT 701 Final Topics Eric Slud 5/9/2023
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Bickel & Doksum Coverage
(1) Confidence Intervals -- Duality with Hypothesis Tests, Sec.4.5
Bayesian Credible Intervals, Sec. 4.7
(2) Likelihood Ratio Tests, Sec. 4.9
Large Sample approximations (using CLT) to UMP one-sided tests
Power of One-parameter tests at Local Alternatives
(3) MLE Large Sample Theory, Canonical Exponential Families Sec.5.2.1, 5.3.3
"Usual regularity conditions", Sec. 5.4 and 6.2.1-6.2.2
MLE large-sample distribution Theory, Consistency and Efficiency, Secs. 5.2.2, 5.4.2
Delta Method, Sec. 5.3.
Bernstein-von Mises Theorem, Sec. 5.5 and 6.2.3
(4) Gaussian Linear Models, Sec. 6.1; Canonical Forms and Projections
(5) Asymptotics for Estimating Equation Estimators and MLEs in Higher Dimensions, Sec. 6.2
Wilks Theorem, Asymptotic Equivalence between Wald, Rao-Score, and LRT, Sec.6.3
(6) Multinomial and Chi-square Goodness of Fit Tests as Applications of LRTs, Sec. 6.4.1
EM Algorithm out of scope for Final, BUT
Newton Raphson and Asymptotic Equivalence of One-Step NR
(starting from consistent asymptotically normal estimator) are In scope
STAT 701 Final Example Problems, Spring 2023
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SampFinProbsF14.pdf, Problems (I)-(III) and (IV).(i)
SampTst1S02.pdf, problems 4, 8
smpFinal.pdf (from 2002), problems (1)--(4)
SampS09.pdf, all problems
SampFinS09.pdf, all problems
SampFinS10.pdf, all problems
SampTst1S10.pdf, problems (I), (IV)
SampTst2S10.pdf, all problems