Foundations of Statistical Inference

This course provides an introduction to modern statistical inference with theory and applications. Students will learn the mathematical theory of statistical inference with an understanding of its applications. Limiting distributions and limit theorems, empirical distribution functions, bootstrap methods, parametric point estimation (including maximum likelihood estimators and Bayes estimation), confidence intervals, sufficiency and exponential families, and generalized linear models in exponential families with applications to linear regression and logistic regression are all covered. Tests of hypothesis, likelihood ratio tests, UMP tests, and tests in regression analysis are further developed. Literature on recent problems and methods in statistics are also examined.