Open Access
September, 1991 The Singularities of Fitting Planes to Data
Steven P. Ellis
Ann. Statist. 19(3): 1661-1666 (September, 1991). DOI: 10.1214/aos/1176348269


Plane-fitting, for example, linear regression, principal components or projection pursuit, is treated from a general perspective. It is shown that any method of plane-fitting satisfying very mild hypotheses must have singularities, that is, data sets near which the procedure is unstable. The well-known collinearity phenomenon in least squares regression is a special case. Severity of singularities is also discussed. The results, which are applications of algebraic topology, may be viewed as putting limits on how much can be done through robustification to stabilize plane-fitting.


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Steven P. Ellis. "The Singularities of Fitting Planes to Data." Ann. Statist. 19 (3) 1661 - 1666, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62059
MathSciNet: MR1126345
Digital Object Identifier: 10.1214/aos/1176348269

Primary: 62H99
Secondary: 62J05

Keywords: collinearity , Linear regression , principal components , Projection pursuit

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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