Abstract
Nonlinear principal components are defined for normal random vectors. Their properties are investigated and interpreted in terms of the classical linear principal component analysis. A characterization theorem is proven. All these results are employed to give a unitary interpretation to several different issues concerning the Chernoff-Poincaré type inequalities and their applications to the characterization of normal distributions.
Original language | English |
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Pages (from-to) | 652-660 |
Number of pages | 9 |
Journal | Journal of Multivariate Analysis |
Volume | 100 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2009 |
Keywords
- 47A75
- 49R50
- 60E05
- 62H25
- Chernoff inequality
- Hermite polynomials
- Nonlinear principal components
- Normal distributions
- primary
- secondary