INTRODUCTION TO FUNCTIONAL DATA ANALYSIS WITH R

INTRODUCTION TO FUNCTIONAL DATA ANALYSIS WITH R

Date

11 – 15 June 2018

Location

Aula A1 del Centre de Recerca Matemàtica (CRM)

Summary

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.

Potential participants

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

Free of charge places are available in this course for BGSMath PhD and postdocs.If you are interested, please send a message to secretariat@bgsmath.cat .

 

Minimum requirements and assessment criteria

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

 

Date

11 – 15 June 2018

Location

Aula A1 del Centre de Recerca Matemàtica (CRM)

Summary

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.

Potential participants

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

Free of charge places are available in this course for BGSMath PhD and postdocs.If you are interested, please send a message to secretariat@bgsmath.cat .

 

Minimum requirements and assessment criteria

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

 

Course organized by Servei d’Estadística Aplicada with the support of the BGSMath, through the ”María de Maeztu” Programme for Units of Excellence in R&D” (MDM‐2014‐0445).

Lecturers

Pedro F. Delicado Useros
Departament d’Estadística i Investigació Operativa
Universitat Politècnica de Catalunya

Manuel Febrero Bande
Dpto. de Estatística, Análise Matemática e Optimización
Área de Estadística e Investigación Operativa
Facultad de Matemáticas
Universidad de Santiago de Compostela

Contents

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

References

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. https://cran.r-project.org/web/packages/fda/

Shedule

Monday, 11 June

15h – 18h
Pedro Delicado: Introduction to Functional Data Analysis (FDA).

Tuesday, 12 June

10h – 13h
Pedro Delicado: Observed functional data and its computational representation.

Lunch (not included)

15h – 18h
Pedro Delicado: Exploratory analysis of functional data.

Wednesday, 13 June

10h – 13h
Pedro Delicado: Dimensionality reduction.

Lunch (not included)

15h – 18h
Manuel Febrero: Regression with functional data.

Thursday, 14 June

10h – 13h
Manuel Febrero: Regression with functional data.

Lunch (not included)

15h – 18h
Manuel Febrero: Classification techniques.

Friday, 15 June

10h – 13h
Manuel Febrero: Hypothesis testing.

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