This course introduces the students to the fundamental principles of modern graduate level statistical theory with a strong emphasis on conceptual aspects of estimation theory and statistical inference along with an exploration of the modern computational techniques needed in the application/implementation of the methods covered. Topics include fundamentals of probability theory for statistics random variable with a focus on the understanding and use of probability distribution function (both probability density function and cumulative distribution function) quantiles of a distribution understanding and use of the mathematical expectation operator special discrete and continuous distributions and distributions of functions of random variables and their use in statistical modelling sums of random variables as used in statistics point estimation limit theorems properties of estimators (bias variance mean squared error consistency efficiency sufficiency) bias variance trade-off interval estimation hypothesis testing bootstrap approach to estimation and inference and elements of computational statistics.

Fundamentals of Statistical Theory

Upcoming