This course will broadly cover topics from the area of functional data analysis, exploring theory and applications. The approach this module will take is based on the Hilbert Space formalism and is concerned with statistical hypothesis tests in various functional data analytic settings. Theory will be motivated by examples from various areas of science including engineering, chemistry and finance.

Below you can find the course outline. Every week a new set of lecture notes will be added. At the end of each lecture, video recordings (hosted on Youtube), script from my virtual blackboard and any R code I wrote during the session will be made available. At the bottom of this page you can find more details on assessment, reading list, prerequisites, format etc.

The lecture plan is as follows.

• Week 1: Lecture Notes | R Code for Reconstructing Curves | R Code for Curve Registration
  • Introduction to FDA: what is functional data, some elements from the FDA toolkit.
  • Smoothing and Regularisation.

Deadline: TBC

Details: TBC

Relevant introductory graduate textbooks and edited volumes:

• Horváth, Lajos, and Kokoszka, Piotr. Inference for functional data with applications. Vol. 200. Springer Science & Business Media, 2012.
• Kokoszka, Piotr, and Matthew Reimherr. Introduction to functional data analysis. CRC Press, 2017.
• Hsing, Tailen, and Randall Eubank. Theoretical foundations of functional data analysis, with an introduction to linear operators. Vol. 997. John Wiley & Sons, 2015.
• Ramsey, J.O., Silverman, B.W., Functional Data Analysis, Springer Series in Statistics, 2005.
• Ramsay, James O., and Bernard W. Silverman. Applied functional data analysis: methods and case studies. Springer, 2007

• Basic knowledge of Statistics and Probability.
• Familiarity or some exposure to function spaces will be useful

• There will be optional exercises spread throughout the lecture notes. There will be no separate problem sheets. Some problems will require the use of some programming.

• Andrew Duncan, Imperial College

• Email: a.duncan at imperial.ac.uk

• website: http://wwwf.imperial.ac.uk/~aduncan/