Math 494 - Schedule

# Schedule

### Schedule of topics: Math 494

Date Chapter       Description
Jan 19      1.9 Introduction, mgfs, and review
Jan 21 1.9, 2.5, 3.1 More mgfs

Jan 24 3.4 Normal random variables: sums and CLT
Jan 26 3.3 The Gamma distribution and friends
Jan 28 3.3, 3.6 The Chi squared and Student t-distributions

Jan 31 3.6, 4.1 Moments of t-distributions, sample distributions
Feb 2 3.6 t-distributions from samples and the t-test
Feb 4 3.6 F-distributions, homework solutions

Feb 7 3.4.1, 3.7, 4.1  Mixture distributions, Statistics
Feb 9 4.1, 5.1 Unbiased estimator examples
Feb 11 5.1 Confidence intervals

Feb 14 5.1, 5.2 More confidence intervals, order statistics
Feb 16 5.2 Order statistic pdfs and joint pdfs
Feb 18 5.2 Order statistics as estimators

Feb 21 5.7 Chi-squared statistics
Feb 23 5.7 Chi-squared statistics -- GOF
Exam 1 due
Feb 25 5.7 Chi-squared statistics -- independence

Feb 28 6.1 Maximum likelihood -- Bernoulli example
Mar 2 6.1 Maximum likelihood -- asymptotic maximality of theta_real
Mar 4 6.1 Mle examples

Mar 7 6.1 Mles are preserved under 1-1 transformations
Mar 9 6.1 Statement of convergence of mles -> theta_real
Mar 11 6.1 Proof of convergence of mles -> theta_real

Mar 14 Spring Break! (no class)
Mar 16 Spring Break! (no class)
Mar 18 Spring Break! (no class)

Mar 21 6.2 Overview of 6.2 ideas
Mar 23 6.2 Score functions and Fisher information
Mar 25 6.2 Fisher information example, statement of Rao-Cramer

Mar 28 6.2 Proof of Rao-Cramer, Bernoulli examples
Mar 30 6.2 CLT for mles, proof (Andy Womack)
Apr 1 6.2 CLT for mles and KL divergence (Andy Womack)

Apr 4 6.2 what (R5) means, and how to check it
Apr 6 6.2 the big ideas in the CLT for mles proof
Exam 2 due
Apr 8 6.2 Asymptotic efficiency, ARE

Apr 11 6.2 ARE examples: Laplace and normal
Apr 13 6.2 hw solutions
Apr 15 6.2 Differentiating under the integral sign (Kabe Moen)

Apr 18 6.3 Wald tests, likelihood ratio test
Apr 20 6.3 Likelihood ratio statistic, asymptotic distribution
Apr 22 6.3 Scores test, asymptotic equivalency of likelihood tests

Apr 25 6.4 2-parameter mles for normal random variables
Apr 27 6.4 2-parameter Fisher information for normals, CLT for medians
Apr 29 - CLT for medians

May 9 Final exam   (6:00 pm - 8:00 pm, January 110)

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