DESCRIPTION: The objective of this class is to gain an understanding of fundamental mathematical concepts in modern statistics. This course is the first part of a two-semester sequence that presents an integrated overview of finite sample and asymptotic statistics.
The main body of the class will be devoted to the detailed theoretical treatment of point estimation and some of its implications to testing. Three general philosophies of estimation, and their inter-connections, will be treated in detail: maximum likelihood, Bayes, and minimax. The properties of estimators will be evaluated via a number of modalities: their efficiency and, closely connected, their risk, and their limiting distributions.
Additional topics include: introduction to testing hypotheses, asymptotic testing based on the maximum likelihood estimator.
PREREQUISITES: Undergraduate real analysis, probability and statistics (MATH 3110, MATH 4710/STSCI 3080, STSCI 4090); or permission of the instructor.
GRADING: Letter
CREDITS: 4