S625: Nonparametric Theory And Data Analysis
Survey of methods for statistical inference that do not rely on parametric probability models. Statistical functionals, bootstrapping, empirical likelihood. Nonparametric density and curve estimation. Rank and permutation tests.
Semester(s) Offered: Fall
Class time: Tuesday, Thursday : 4:00-5:15
Instructor: Qingsong Shan - email@example.com
Other Contact(s): Qingsong Shan - firstname.lastname@example.org
Prerequisites: College-level probability (e.g. M463) and statistics with computing (e.g. S520)
Algebra Required?: Some notion of matrix algebra is useful
Calculus Required?: Some notion of integration is useful
Recommended follow-up classes: machine learning
Books used: Lecture Notes.
Applied/Theoretical: Somewhat more applied than theoretical.
Formal Computing Lab?: No
Software Used: R
How the software is used: The software is mainly used for computation and data analysis.
Problem Sets: Weekly
Data Analysis: Yes
Keywords: Nonparametric, bootstrap, permutation test, density estimation, curve estimation
Comments: The course is an introduction to statistics outside of the "classical" techniques. Over and above the material itself, the course is useful for reinforcement of and elaboration on concepts of testing and estimation seen in classical courses, and serves as a bridge to modern, computationally intensive branches of statistics like machine learning.