After covering necessary matrix tools and reviewing mathematical analysis topics such as Taylor series and orders of magnitude, this course will delve into the theory of advanced statistics, including topics such as sufficiency, completeness, ancillary statistics, invariance, likelihood-based inference, estimating functions, large sample theory, and Edgeworth and saddlepoint approximations.

Upon successful completion of the course, students will be able to:

  • Use rigorous mathematical techniques to derive mathematical statistics results, including construction of hypothesis tests and confidence intervals
  • Describe and program optimization algorithms used in estimation
  • Compare and contrast different statistical inference approaches based on principles of mathematical statistics
  • Derive asymptotic distributions and properties of statistics
  • Communicate summaries of journal articles on mathematical statistics topics, both written and oral

Course Information

Log into D2L course page to access course material, assignments, etc.

Data Sets

  • Challenger O-ring data (.txt) and description
  • Robots data (Homework 3)
  • Epilepsy data from Fitzmaurice, Laird, and Ware (2011)