A multivariate version of Samuelson’s inequality

According to Samuelson’s inequality, the deviation of any particular observation from the mean is bounded by a multiple of standard deviation. In this paper we consider some properties of a multivariate extension of this result.

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Bibliographic Details
Published inLinear algebra and its applications Vol. 410; pp. 143 - 149
Main Authors Trenkler, Götz, Puntanen, Simo
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 15.11.2005
Elsevier Science
Subjects
Algebra
Covariance matrix
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mahalanobis distance
Mathematics
Matrix inequalities
Orthogonal projector
Probability and statistics
Sample mean
Sample variance
Sciences and techniques of general use
Statistics
Sample variance
Matrix inequalities
15A45
62H20
Sample mean
Covariance matrix
Orthogonal projector
Mahalanobis distance
Statistical analysis
Matrix inequality
Variance
Orthogonal projection
15A45 Covariance matrix
Standard deviation
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Summary:According to Samuelson’s inequality, the deviation of any particular observation from the mean is bounded by a multiple of standard deviation. In this paper we consider some properties of a multivariate extension of this result.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2005.02.032