The Annals of Statistics

Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample

Masashi Okamoto

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Abstract

This paper shows that a quadratic form in a multivariate sample has a certain rank and its nonzero eigenvalues are distinct with probability one under the assumption that the matrix defining the quadratic form satisfies a certain rank condition and that the underlying distribution of the sample is absolutely continuous with respect to Lebesgue measure.

Article information

Source
Ann. Statist., Volume 1, Number 4 (1973), 763-765.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342472

Digital Object Identifier
doi:10.1214/aos/1176342472

Mathematical Reviews number (MathSciNet)
MR331643

Zentralblatt MATH identifier
0261.62043

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62E15: Exact distribution theory

Keywords
Distinctness of eigenvalues quadratic form in a multivariate sample

Citation

Okamoto, Masashi. Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample. Ann. Statist. 1 (1973), no. 4, 763--765. doi:10.1214/aos/1176342472. https://projecteuclid.org/euclid.aos/1176342472


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