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UNEXPECTED PROPERTIES OF BANDWIDTH CHOICE WHEN SMOOTHING DISCRETE DATA FOR CONSTRUCTING A FUNCTIONAL DATA CLASSIFIER.

Raymond J Carroll1, Aurore Delaigle2, Peter Hall2

  • 1Department of Statistics Texas A&M University College Station, Texas 77843 USA carroll@stat.tamu.edu.

Annals of Statistics
|October 14, 2014
PubMed
Summary

Functional data analysis (FDA) smoothing is effective for prediction but not classification. Undersmoothing is often preferred for classification, but optimal smoothing depends on complex error rate properties.

Keywords:
Centroid methoddiscriminationkernel smoothingquadratic discriminationsmoothing parameter choicetraining data

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Functional data analysis (FDA) typically uses smoothing appropriate for approximating underlying smooth functions.
  • This approach is well-established and optimal for prediction and hypothesis testing in FDA.

Purpose of the Study:

  • To investigate the effectiveness of standard FDA smoothing techniques in classification problems.
  • To identify optimal smoothing strategies for functional data classification.

Main Methods:

  • The study analyzes error rates as functions of smoothing parameters in classification.
  • It examines the impact of smoothing training data versus test data.
  • Investigates the influence of bandwidth selection on classification performance.

Main Results:

  • Standard smoothing approaches effective for prediction are suboptimal for classification.
  • Undersmoothing is often desirable, but with significant qualifications.
  • The impact of smoothing training data can outweigh smoothing test data.
  • Optimal smoothing is not universally undersmoothing; large bandwidths can be superior in some cases.
  • Perverse results stem from unusual properties of error rates concerning smoothing parameters.

Conclusions:

  • Classification with functional data requires different smoothing strategies than prediction or hypothesis testing.
  • The choice of smoothing parameter is highly sensitive and context-dependent in functional data classification.
  • Further research into the nuanced behavior of error rates in functional classification is warranted.