Detail publikace

Optimal singular correlation matrices estimated when sample size is less than the number of random variables

VOŘECHOVSKÝ, M.

Originální název

Optimal singular correlation matrices estimated when sample size is less than the number of random variables

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

Correlation matrix, error norm, singular matrix, positive semidefinitness, mechanical analogy, Toeplitz matrix, correlation control

Klíčová slova v angličtině

Correlation matrix, error norm, singular matrix, positive semidefinitness, mechanical analogy, Toeplitz matrix, correlation control

Autoři

VOŘECHOVSKÝ, M.

Rok RIV

2012

Vydáno

8. 11. 2012

Nakladatel

Elsevier

Místo

Spojené království Velké Británie a Severního Irska

ISSN

0266-8920

Periodikum

PROBABILISTIC ENGINEERING MECHANICS

Ročník

2012 (30)

Číslo

1

Stát

Spojené království Velké Británie a Severního Irska

Strany od

104

Strany do

116

Strany počet

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"
}