Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix

Wiktor Oktaba; Andrzej Kieloch

Applications of Mathematics (1993)

  • Volume: 38, Issue: 1, page 61-66
  • ISSN: 0862-7940

Abstract

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This paper concerns generalized quadratic forms for the multivariate case. These forms are used to test linear hypotheses of parameters for the multivariate Gauss-Markoff model with singular covariance matrix. Distributions and independence of these forms are proved.

How to cite

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Oktaba, Wiktor, and Kieloch, Andrzej. "Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix." Applications of Mathematics 38.1 (1993): 61-66. <http://eudml.org/doc/15736>.

@article{Oktaba1993,
abstract = {This paper concerns generalized quadratic forms for the multivariate case. These forms are used to test linear hypotheses of parameters for the multivariate Gauss-Markoff model with singular covariance matrix. Distributions and independence of these forms are proved.},
author = {Oktaba, Wiktor, Kieloch, Andrzej},
journal = {Applications of Mathematics},
keywords = {inultivariate general linear Gauss-Markoff model; Wishart distribution; multinormal distribution; set of linear estimable parametric functions; quadratic form; singular covariance matrix; multivariate general linear Gauss-Markoff model; Wishart distribution; multi-normal distribution; linear estimable parametric functions; generalized quadratic forms; linear hypotheses; singular covariance matrix; independence},
language = {eng},
number = {1},
pages = {61-66},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix},
url = {http://eudml.org/doc/15736},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Oktaba, Wiktor
AU - Kieloch, Andrzej
TI - Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 1
SP - 61
EP - 66
AB - This paper concerns generalized quadratic forms for the multivariate case. These forms are used to test linear hypotheses of parameters for the multivariate Gauss-Markoff model with singular covariance matrix. Distributions and independence of these forms are proved.
LA - eng
KW - inultivariate general linear Gauss-Markoff model; Wishart distribution; multinormal distribution; set of linear estimable parametric functions; quadratic form; singular covariance matrix; multivariate general linear Gauss-Markoff model; Wishart distribution; multi-normal distribution; linear estimable parametric functions; generalized quadratic forms; linear hypotheses; singular covariance matrix; independence
UR - http://eudml.org/doc/15736
ER -

References

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  1. Mardia K. V., Kent J. T., Bibby J. M., Multivariate Analysis, Academic Press, London, 1979. (1979) Zbl0432.62029MR0560319
  2. Oktaba W., Estimation of the parametric functions in the multivariate general Gauss-Markoff model, XV Colloquium Metodol., Agrobiom., Pol. Acad. Sci., Warsaw, 1985, pp. 178-182. (In Polish.) (1985) 
  3. Rao C. R., Linear Statistical Inference and Its Applications, sec. ed., J. Wiley, New York, 1973. (1973) Zbl0256.62002MR0346957
  4. Rao C. R., Mitra S. K., Generalized Inverse of Matrices and its Applications, J. Wiley, New York, 1971. (1971) Zbl0236.15005MR0338013
  5. Roy S. N., Some aspects of multivariate analysis, Indian Statistical Institute, New York, Calcutta, 1957. (1957) MR0092296
  6. Seber G. А. F., Multivariate Observations, J. Wiley, New York, 1984. (1984) Zbl0627.62052MR0746474
  7. Srivastava M. S., Khatri C. G., An Introduction to Multivariate Statistics, Elsevier North Holland, Inc., New York, 1979. (1979) Zbl0421.62034MR0544670

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