STATISTICAL PROBLEMATICS

What can we do when we have at hand a functional dataset? This webpage proposes to answer to this question by listing various statistical problematics presented in this website (references of chapters and parts are those of our NPFDA book).

What can we do with:

1. only a population of curves?

   Answer: predicting an unobserved categorical response from a curve:
   UNSUPERVISED CLASSIFICATION (i.e. CLUSTERING)
   (see CHAPTER 9 for more details on the nonparametric functional classification method)
   • 
     Classifying radar waveforms (satellite dataset)
     • Description of the analysis (pdf)
     • R/S-plus commandlines (plain text)
   • 
     Classifying spectrometric curves
     • Description of the analysis(pdf)
     • R / S-plus commandlines (plain text)
   
   

2. a population of curves and corresponding categorical responses?

   Answer: predicting a categorical response from a curve:
   SUPERVISED CLASSIFICATION (i.e. CURVES DISCRIMINATION)
   (see CHAPTER 8 for more details on the nonparametric functional discrimination method)
   • 
     Discriminating phoneme log-periodograms
     • Description of the analysis (pdf)
     • R/S-plus commandlines (plain text)
   • 
     Discriminating spectrometric curves
     • Description of the analysis(pdf)
     • R commandlines (plain text)
   
   

3. a population of curves and corresponding scalar responses?

   Answer: predicting a scalar response from a curve via three functional methods:
   functional conditional EXPECTATION (regression),
   functional conditional MEDIAN,
   functional conditional MODE
   (see PART II for more details on the nonparametric functional prediction methods)
   • 
     Predicting fat content from spectrometric curves
     • Description of the analysis (pdf)
     • R/S-plus commandlines (plain text)
   
   

4. a time series?

   Answer: forecasting a future value via three functional methods:
   functional conditional EXPECTATION (regression),
   functional conditional MEDIAN,
   functional conditional MODE
   (see PART IV for more details on the nonparametric functional methods for forecasting)
   • 
     Forecasting electricity consumption
     • Description of the analysis(pdf)
     • R/S-plus commandlines (plain text)
   • 
     Forecasting sea surface temperatureElnino time series
     • Description of the analysis(pdf)
     • R/S-plus commandlines (plain text)