Class Time: Wednesday and Friday 4:15-5:30pm. Place: Room 107, 24 Hillhouse Ave.
Course Description: Data in the form of observed functions (curves and surfaces) arise in applications including growth analysis, meterology, economics, and medicine. This course will present ideas and techniques for the statistical analysis of such data. Included are smoothing methods (wavelets, Fourier series, and splines), will cover one topic each week, with one lecture for introducing real data, and the other lecture for methodology and theory. Additional topics in asymptotics analysis as time permits. Knowledge of statistical theory at the level of Statistics 542b is assumed.
A presentation (data analysis of the examples in my lectures or your own research): 60%
Topic 1: Life course data in Criminology. Variance stabilization transformation. Smoothing. Cross-validation. Principal component analysis. Regularized principal component analysis.
Topic 2: Reaction-Time data for attention deficit disorder. Human growth data. Constrained smoothing: fitting positive functions, fitting monotone function.
Topic 3: Bone shape data from a paleopathology study. Canonical correlation analysis. Linear discriminant analysis. Varimax method. Regularized discriminant analysis.
Topic 4: Handwriting data. Curve registration.
Topic 5: Lip acceleration from Electromyography. Canadian weather data. Functional linear model with scalar or functional responses.
Topic 6: Juggling data. (Simple) Differential equation modelling. Principal differential analysis. Parameter estimation for differential equations.
Topic 7: Chemometric Data. Nonparametric classification of functional data.
Topic 8: Some perspectives on Functional Data Analysis