140.771.01 ADVANCED STATISTICAL THEORY I

Examines statistics as a discipline along the path towards making decisions. First examines the justification of statistics from axioms on informed preferences and its close connection to Bayesian theory, and then examines the role of standardizing intermediate steps, through various additional restrictions on estimation, and studies the properties of the resulting methods.

Upon successful completion of this course, students will: 1) be introduced to the role of statistics as a path towards inference and making decisions; 2) understand basic decision theory, including the properties of Bayes rules and other ordering of decision strategies; 3) justify decision theory on simple axioms, and examine reasons for studying restricted estimation strategies; 4) examine properties of unbiased estimation and functions.