STATS 3D03, Fall 2018
This is a course on mathematical statistics in which students will learn the theoretical foundations underlying statistical inference methods and concepts. The course will start with a review of the axioms of probability in a more formal mathematical framework than studied in STATS 2D03. This will include classical probability of events and Bayes Theorem. Random variables and expectations will be formally derived and the properties of general expectations will be studied including the moment generating function (MGF), its properties and uses. Of particular interest will be the use of the MGF in deriving the distribution of functions of random variables. Bivariate and general mutivariate random vectors will be introduced and general techniques introduced to find the distribution of statistics derived from random samples. Important concepts of convergence of sequences of random variables will also be introduced and studied. The remainder of the course will focus on inferential statistics. Students will learn key concepts for confidence intervals including derivation of general intervals based on pivotal quantites and the properties of such intervals. They shall also learn key concepts and methods for testing of statistical hypotheses. The course will end with a study of likelihood based inference including the use of limiting distributions applicable for large sample sizes.
INSTRUCTOR: A. Canty
3 UnitsMultivariate distributions; distributions related to normal inference; point estimation; sampling distributions; consistency and limiting distributions; interval estimation; hypothesis testing; single parameter maximum likelihood methods; Rao-Cramer Lower Bound and Efficiency.
Three lectures; one term
Prerequisite(s): STATS 2D03 and one of ISCI 2A18 A/B, MATH 2A03, 2L03, 2Q04, 2X03, 2ZZ3
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS