THE SINGULARITIES OF FITTING PLANES TO DATA
成果类型：
Article
署名作者：
ELLIS, SP
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348269
发表日期：
1991
页码：
1661-1666
关键词：
摘要：
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 is 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.