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07 February 2025 |
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Article overview
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A note on the variance in principal component regression | Bert van der Veen
; | Date: |
4 Jan 2023 | Abstract: | Principal component regression is a popular method to use when the predictor
matrix in a regression is of reduced column rank. It has been proposed to
stabilize computation under such conditions, and to improve prediction accuracy
by reducing variance of the least squares estimator for the regression slopes.
However, it presents the added difficulty of having to determine which
principal components to include in the regression. I provide arguments against
selecting the principal components by the magnitude of their associated
eigenvalues, by examining the estimator for the residual variance, and by
examining the contribution of the residual variance to the variance of the
estimator for the regression slopes. I show that when a principal component is
omitted from the regression that is important in explaining the response
variable, the residual variance is overestimated, so that the variance of the
estimator for the regression slopes can be higher than that of the ordinary
least squares estimator. | Source: | arXiv, 2301.01543 | Services: | Forum | Review | PDF | Favorites |
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