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The Impact of Measurement Error on Principal Component Analysis

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  • Kristoffer Herland Hellton
  • Magne Thoresen

Abstract

type="main" xml:id="sjos12083-abs-0001"> We investigate the effect of measurement error on principal component analysis in the high-dimensional setting. The effects of random, additive errors are characterized by the expectation and variance of the changes in the eigenvalues and eigenvectors. The results show that the impact of uncorrelated measurement error on the principal component scores is mainly in terms of increased variability and not bias. In practice, the error-induced increase in variability is small compared with the original variability for the components corresponding to the largest eigenvalues. This suggests that the impact will be negligible when these component scores are used in classification and regression or for visualizing data. However, the measurement error will contribute to a large variability in component loadings, relative to the loading values, such that interpretation based on the loadings can be difficult. The results are illustrated by simulating additive Gaussian measurement error in microarray expression data from cancer tumours and control tissues.

Suggested Citation

  • Kristoffer Herland Hellton & Magne Thoresen, 2014. "The Impact of Measurement Error on Principal Component Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1051-1063, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1051-1063
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    File URL: http://hdl.handle.net/10.1111/sjos.12083
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    References listed on IDEAS

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    1. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    2. Jianqing Fan & Jinchi Lv & Lei Qi, 2011. "Sparse High-Dimensional Models in Economics," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 291-317, September.
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