The Annals of Statistics

The Singularities of Fitting Planes to Data

Steven P. Ellis

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 19, Number 3 (1991), 1661-1666.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348269

Digital Object Identifier
doi:10.1214/aos/1176348269

Mathematical Reviews number (MathSciNet)
MR1126345

Zentralblatt MATH identifier
0729.62059

JSTOR
links.jstor.org

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62J05: Linear regression

Keywords
Projection pursuit linear regression principal components collinearity

Citation

Ellis, Steven P. The Singularities of Fitting Planes to Data. Ann. Statist. 19 (1991), no. 3, 1661--1666. doi:10.1214/aos/1176348269. https://projecteuclid.org/euclid.aos/1176348269


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