# Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model

Applications of Mathematics (1995)

- Volume: 40, Issue: 1, page 47-54
- ISSN: 0862-7940

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topOktaba, Wiktor. "Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model." Applications of Mathematics 40.1 (1995): 47-54. <http://eudml.org/doc/32902>.

@article{Oktaba1995,

abstract = {The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. $1^\circ $ determinant ratios as products of independent chi-square distributions, $2^\circ $ moments for the determinants and $3^\circ $ the method of obtaining approximate densities of the determinants.},

author = {Oktaba, Wiktor},

journal = {Applications of Mathematics},

keywords = {products of independent chi-squares; multivariate general linear Gauss-Markoff model; wishart distribution; singular covariance matrix; set of linear parametric functions; moment of determinant ratio; approximate simultaneous confidence interval; Wishart distribution; linear parametric functions; approximate simultaneous confidence interval; general multivariate Gauss-Markov model; singular covariance matrix; determinant ratios; products of independent chi-square distributions; moments; determinants},

language = {eng},

number = {1},

pages = {47-54},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model},

url = {http://eudml.org/doc/32902},

volume = {40},

year = {1995},

}

TY - JOUR

AU - Oktaba, Wiktor

TI - Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model

JO - Applications of Mathematics

PY - 1995

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 40

IS - 1

SP - 47

EP - 54

AB - The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. $1^\circ $ determinant ratios as products of independent chi-square distributions, $2^\circ $ moments for the determinants and $3^\circ $ the method of obtaining approximate densities of the determinants.

LA - eng

KW - products of independent chi-squares; multivariate general linear Gauss-Markoff model; wishart distribution; singular covariance matrix; set of linear parametric functions; moment of determinant ratio; approximate simultaneous confidence interval; Wishart distribution; linear parametric functions; approximate simultaneous confidence interval; general multivariate Gauss-Markov model; singular covariance matrix; determinant ratios; products of independent chi-square distributions; moments; determinants

UR - http://eudml.org/doc/32902

ER -

## References

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- Some Aspects of Multivariate Analysis, New York, 1957. (1957)
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- Generalized inverse and confidence estimation by least squares method, Trabajos De. Estadistica Y de Investigation Operativa 21, Cuadermos 1 y 2 Afio, Iberica, Tarragona 1970 vol. 34, Madrid, 1968, pp. 115–120. (1968)

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