Asymptotic Tools

Catalog description

An advanced theoretical course on statistical large sample theory and its application in biomedical and public health research. This is an advanced theoretical course on statistical large sample theory and its application in biomedical and public health research. Students are expected to understand the theorems and proofs on large sample theory, and conduct statistical derivation and asymptotic inference by applying the knowledge from the course. Important asymptotic statistics ideas on basic probability theory, statistical large sample theory, and efficient estimation and testing are covered in this course. Specific topics include the modes of convergence, the law of large numbers, Taylor's theorem and delta method, order statistics, central limit theorem, U-statistics, likelihood inference, M-estimates, L-estimates, efficiency of test, goodness of fit, Bootstrap and Jackknife estimates, and permutation and rank tests. In addition, statistical computing is vital for understanding asymptotic theory so program techniques based on R/SAS software are learned and utilized during the course. Students are expected to have taken at least two graduate level courses in mathematical statistics.