Introduction to Functional Data Analysis with R

Introduction to Functional Data Analysis with R


Functional data arise when one of the variables of interest in a data set can be seen naturally as a smooth curve or function. Functional Data Analysis (FDA) can then be thought of as the statistical analysis of samples of curves. In the last two decades, FDA techniques have evolved rapidly, which has allowed the FDA to reach a remarkable methodological maturity. Many standard statistical methods have been adapted to functional data: regression models (lm, glm, non-parametric regression, ...), multivariate analysis (PCA, MDS, Clustering, Depth measures, ...), time series, spatial statistics, among other. At the same time, its methods have been applied to quite broadly in medicine, science, business, engineering, demography and social sciences, etc. This course offers an introduction to FDA and presents some of the R libraries oriented to this type of data. The aim is that at the end of the course the students are able to identify situations in which they can treat their data as functional, to represent them computationally, to apply simple FDA techniques (descriptions, dimensionality reduction, regression) and to visualize the results.


  1. Introduction to Functional Data Analysis (FDA).
    • An overview of FDA.
    • Concepts of Functional Analysis useful in FDA.
  2. Observed functional data and its computational representation.
    • Developments in bases of functions.
    • Smoothing: Kernel, Local Polynomials, Splines.
    • Registration and transformations of functional data.
  3. Exploratory analysis of functional data.
    • Location and dispersion statistics.
    • Depth measurements.
    • Outliers detection.
  4. Dimensionality reduction.
    • Functional Principal Components.
    • Multidimensional Scaling.
  5. Regression with functional data.
    • Scalar response.
    • Functional response.
    • Conditional median, conditional quantiles.
    • ANOVA.
    • Treatment of covariates.
  6. Classification techniques.
    • Supervised classification.
    • Unsupervised classification.
  7. Hypothesis testing.


Identificación de patrones atípicos de respuesta al ítem mediante análisis de datos funcionales
April, 17th, 2018
There was a introduction to Functional Data Analysis in this seminar
Presentation: link




Pedro F. Delicado Useros. Statistics and Operational Research Department, Universitat Politècnica de Catalunya (

Manuel Febrero Bande. Statistics, Mathematical Analysis and Optimization Department, Universidad de Santiago de Compostela (



Master and PhD students, postdoc researchers and any researcher with interest in the topic.


The students should have basic knowledge of Statistics (e.g. lineal regression) and Multivariate Analysis (principal components or multidimensional scaling).
User-programmer in R.

Organization details:

The Introduction to Functional Data Analysis with R will be held on June 2018, from 11st to 15th, at Aula A1 of the Centre de Recerca Matemàtica (UAB Campus), with next schedule:

Monday, June 11st: from 15h to 18h
Tuesday, Wednesday and Thursday (June 12nd, 13rd and 14th): from 10h to 13h and from 15h to 18h
Friday, June 15th: from 10h to 13h

The course duration is 24 hours.

The minimum number of participants for the course is 10, and the maximum is 20.

Formalize the Pre-registration: link

Once we received your form we will send an email to confirm that either you have an assigned place or you are on the waiting list.


With the support of the BGSMath, through the ”María de Maeztu” Programme for Units of Excellence in R&D” (MDM‐2014‐0445).

Registration fees (2018):

Concept Quantity Import
    External Esfera UAB
(before June 1st)
1 asist 450,00 € 325,00 € 270,00 €
(after June 1st)
1 asist 750,00 € 545,00 € 450,00 €

UAB rate: UAB university community, BGSMath members and students from other universities.
Esfera rate: Agencies, institutions and companies from esfera de la UAB or Public Sector.
External rate: Agencies, institutions and companies from Private Sector.

The rate is assigned by the person/instution/company that made the payment.

- Special discounts for unemployed people, with the apply or renew of the application for unemployment benefits.

- Special discounts for groups of the same comany.

- Grants for Degree of statistic students, see conditions on the registration form.

Not cumulative discounts.

Payment details:

Once the pre-registration is completed you will receive an email informing of the details for the registration payment.

Do wait for our confirmation of the reservation for the course before payment.

Once the payment of the course has been made there will be no refund unless there are circumstances beyond one’s control.


  • Febrero-Bande, M. and M. Oviedo de la Fuente (2012). Statistical computing in functional data analysis: the R package fda.usc. Journal of Statistical Software 51(4), 1-28.
  • Ferraty, F. and P. Vieu (2006). Non parametric functional data analysis. Theory and practice. Springer.
  • Horvath, L. and P. Kokoszka (2012). Inference for functional data with applications. Springer.
  • Kokoszka, P. and M. Reimherr (2017). Introduction to Functional Data Analysis. CRC Press.
  • Ramsay, J. and Silverman, B. (2005). Functional Data Analysis (Second ed.). Springer.
  • Ramsay, J., Wickham, H., Graves, S., and Hooker, G. (2011). fda: Functional data analysis. R package version.
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