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Uncertainty in functional principal component analysis

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  • James Sharpe
  • Nick Fieller

Abstract

Principal component analysis (PCA) and functional principal analysis are key tools in multivariate analysis, in particular modelling yield curves, but little attention is given to questions of uncertainty, neither in the components themselves nor in any derived quantities such as scores. Actuaries using PCA to model yield curves to assess interest rate risk for insurance companies are required to show any uncertainty in their calculations. Asymptotic results based on assumptions of multivariate normality are unsatisfactory for modest samples, and application of bootstrap methods is not straightforward, with the novel pitfalls of possible inversions in order of sample components and reversals of signs. We present methods for overcoming these difficulties and discuss arising of other potential hazards.

Suggested Citation

  • James Sharpe & Nick Fieller, 2016. "Uncertainty in functional principal component analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2295-2309, September.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:12:p:2295-2309
    DOI: 10.1080/02664763.2016.1140728
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