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

Wiktor Oktaba

Applications of Mathematics (1995)

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

Abstract

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

How to cite

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Oktaba, 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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  1. An Introduction to Multivariate Statistical Analysis, J. Wiley, New York, 1958. (1958) Zbl0083.14601MR0091588
  2. A note to confidence estimation by least squares method, Teoria verojatnostej i jejo primeneniya 8 (1963), no. 2, 176. (Russian) (1963) 
  3. 10.1214/aoms/1177703550, Ann. Math. Stat. 35 (1964), no. 2, 475–501. (1964) Zbl0121.36605MR0181057DOI10.1214/aoms/1177703550
  4. Aspects of Multivariate Statistical Theory, J. Wiley, New York, 1982. (1982) Zbl0556.62028MR0652932
  5. Estimation of the parametric functions in the multivariate general Gauss-Markoff model, XV Colloquium Metodol. Agrobiom., Pol. Acad. Sci., Warsaw 1985, pp. 178–182. (Polish) 
  6. Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix, Appl. Math. 38 (1993), 61–66. (1993) MR1202080
  7. Linear Statistical Inference and Its Applications, Sec.  Ed, J. Wiley, New York, 1973. (1973) MR0346957
  8. Some Aspects of Multivariate Analysis, New York, 1957. (1957) 
  9. An Introduction to Multivariate Statistics, Elsevier North Holland, Inc., New York, 1979. (1979) MR0544670
  10. 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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