Course Content:
- Statistical models, Parametric families of distributions, multivariate distributions including the normal, order statistics.
- Data reduction, sufficiency, completeness, exponential families.
- Mixtures, inequalities, convergence concepts, sampling and derived distributions from a normal population.
- Estimation: unbiased estimation, substitution principles, method of moments, least squares, maximum likelihood, asymptotics.
- Comparison of estimators, optimality, information inequality, large sample behavior, consistency, convergence in distribution, asymptotic efficiency.
- Additional topics as time permits.
Prerequisites: Probability at the Math 505a level, or equivalent, multivariate calculus and linear algebra.
Instructor: Larry Goldstein, KAP 406D, larry at math dot usc dot edu, (213) 740-2405
Office Hours: Monday 12:50-1:50, Friday 2-3
Grader: Jerome Grand’Maison
Office Hours: 8-11, Friday at the Math Center
Lecture: 39760R, MWF 11:00 – 11:50, THH 116
Materials
Primary Text: – Statistical Inference, by Casella and Berger, 2nd Edition.
Supplemental References: –
- Statistical Inference by Garthwaite, Jolliffe and Jones, Oxford Scientific.
- A Course in Large Sample Theory, by Ferguson.
- Mathematical Statistics, by Bickel and Doksum
- Asymptotic Statistics, by van der Vaart
- Theory of Point Estimation, by E.L.Lehmann
- Testing Statistical Hypotheses, by E.L.Lehmann
- Linear Regression Analysis, by Seber and Lee
Notes: –
- Notes on Order Statistics
- Wilks on Order Statistics, Bull. Amer. Math. Soc. 54 (1948), 6-50
- Method of Moments
- Estimating Equation Asymptotics
- Deaths by horse and mule kicks in the Prussian Army
- The Epic Story of Maximum Likelihood
Computationally Intensive Techniques:
- Finite Markov Chains and Algorithmic Application. Olle Häggström
- The EM Algorithm and Extensions. McLachlan and Krishnan
- The Jackknife, the Bootstrap and Other Resampling Plans. Bradley Efron