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VOŘECHOVSKÝ, M.
Original Title
Optimal singular correlation matrices estimated when sample size is less than the number of random variables
Type
journal article - other
Language
English
Original Abstract
This paper presents a number of theoretical and numerical results for two norms of optimal correlation matrices in relation to correlation control in Monte Carlo type sampling and the designs of experiments. The optimal correlation matrices are constructed for cases when the number of simulations (experiments) Nsim is less than or equal to the stochastic dimension, i.e. the number of random variables (factors) Nvar. In such cases the estimated correlation matrix cannot be positive definite and must be singular. However, the correlation matrix may be required to be as close to the unit matrix as possible (optimal). The paper presents a simple mechanical analogy for such optimal singular positive semidefinite correlation matrices. Many examples of optimal correlation matrices are given, both analytically and numerically.
Keywords
Correlation matrix, error norm, singular matrix, positive semidefinitness, mechanical analogy, Toeplitz matrix, correlation control
Key words in English
Authors
RIV year
2012
Released
8. 11. 2012
Publisher
Elsevier
Location
Spojené království Velké Británie a Severního Irska
ISBN
0266-8920
Periodical
PROBABILISTIC ENGINEERING MECHANICS
Year of study
2012 (30)
Number
1
State
United Kingdom of Great Britain and Northern Ireland
Pages from
104
Pages to
116
Pages count
13
BibTex
@article{BUT96655, author="Miroslav {Vořechovský}", title="Optimal singular correlation matrices estimated when sample size is less than the number of random variables", journal="PROBABILISTIC ENGINEERING MECHANICS", year="2012", volume="2012 (30)", number="1", pages="104--116", issn="0266-8920" }