STAT 701 Final Topics                     Eric Slud 5/12/2025
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Bickel & Doksum Coverage

(1) Confidence Intervals -- Duality with Hypothesis Tests,  Sec.4.5

(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) Projections of X on span(Y) for jointly distributed Gaussian Variables

(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