Publication detail

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

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

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

Authors

VOŘECHOVSKÝ, M.

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"
}