Introduction to functional data analysis

Organised by
The course is free of charge. Those who wish to attend are kindly requested to email Simona Milani  until 12 October.

Professor Laura M. Sangalli – MOX, Dept. of Mathematics, Politecnico di Milano.
Professor Simone Vantini – MOX, Dept. of Mathematics, Politecnico di Milano.

18 hours (6 three-hour lectures)

CNR Area della Ricerca Milano 1, via Alfonso Corti 12, Milano, Aula Expo

From 14 October to 4 November 2016

Teaching Form
The course will consists of theoretical lectures, research examples, and applicative R sessions. Participants
can bring their laptop computers with their installation of R (see

This is a PhD level course, which will be of interest for those concerned with problems involving functional
data that nowadays arise in several disciplines. Knowledge of the basic principles of statistical inference is
desirable, as well as knowledge of the R computing environment. At the end of the course, participants will
be able to perform standard and more advanced analysis on functional data.

Course program
The course covers classical and advanced models and methods for the statistical analysis of functional data.
Lectures include tutorial sessions with the software R. Many case studies will be
presented, with applications in the life-sciences, earth-sciences, and engineering.

- Introduction to functional data
- From rough data to smooth functions: smoothing and curve fitting
(local polynomials, regression splines, smoothing splines, free-knot splines, wavelets), surface fitting
- Alignment and registration of functional data
- Clustering of functional data
- Dimensional reduction for functional data (functional principal component analysis, functional
independent component analysis, varimax rotations)
- Non-parametric inference for functional data (permutational inference, global and local null hypothesis
testing, functional t-test, functional ANOVA, functional linear regression)

Main reference:
- J.O. Ramsay and B.W. Silverman, Functional Data Analysis, Second Ed., Springer 2005
Additional references:
- J.O. Ramsay and B. W. Silverman, Applied Functional Data Analysis: Methods and Case Studies, Springer
2002.- J.O. Ramsay, G. Hooker and S. Graves, Functional Data Analysis with R and MATLAB, Springer, 2009
- T. Hastie, R. Tibshirani, J. Friedman, The elements of statistical learning, Second Ed., Springer, 2009.
- Pesarin, F. and Salmaso, L.. Permutation Tests for Complex Data: Theory, Applications and Software, Wiley
Series in Probability and Statistics, 2010.

Course schedule
- Friday 14 Oct, 9.30 - 12.30
- Monday 17 Oct, 9.30 - 12.30
- Friday 21 Oct, 9.30 - 12.30
- Tuesday 25 Oct, 9.30 - 12.30
- Friday 28 Oct, 9.30 - 12.30
- Friday 4 Nov, 9.30 - 12.30