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


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: –

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