Seemingly unrelated regression models

Lubomír Kubáček

Applications of Mathematics (2013)

  • Volume: 58, Issue: 1, page 111-123
  • ISSN: 0862-7940

Abstract

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The cross-covariance matrix of observation vectors in two linear statistical models need not be zero matrix. In such a case the problem is to find explicit expressions for the best linear unbiased estimators of both model parameters and estimators of variance components in the simplest structure of the covariance matrix. Univariate and multivariate forms of linear models are dealt with.

How to cite

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Kubáček, Lubomír. "Seemingly unrelated regression models." Applications of Mathematics 58.1 (2013): 111-123. <http://eudml.org/doc/251350>.

@article{Kubáček2013,
abstract = {The cross-covariance matrix of observation vectors in two linear statistical models need not be zero matrix. In such a case the problem is to find explicit expressions for the best linear unbiased estimators of both model parameters and estimators of variance components in the simplest structure of the covariance matrix. Univariate and multivariate forms of linear models are dealt with.},
author = {Kubáček, Lubomír},
journal = {Applications of Mathematics},
keywords = {seemingly unrelated regression; linear statistical model; variance components; BLUE; MINQUE; linear regression; best linear unbiased estimators},
language = {eng},
number = {1},
pages = {111-123},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Seemingly unrelated regression models},
url = {http://eudml.org/doc/251350},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Seemingly unrelated regression models
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 111
EP - 123
AB - The cross-covariance matrix of observation vectors in two linear statistical models need not be zero matrix. In such a case the problem is to find explicit expressions for the best linear unbiased estimators of both model parameters and estimators of variance components in the simplest structure of the covariance matrix. Univariate and multivariate forms of linear models are dealt with.
LA - eng
KW - seemingly unrelated regression; linear statistical model; variance components; BLUE; MINQUE; linear regression; best linear unbiased estimators
UR - http://eudml.org/doc/251350
ER -

References

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  2. Davidson, D., MacKinnon, J. G., Estimation and Inference in Econometrics, Oxford University Press New York (1993). (1993) Zbl1009.62596MR1350531
  3. Kmenta, J., Gilbert, R. F., 10.1080/01621459.1968.10480919, J. Am. Stat. Assoc. 63 (1968), 1180-1200. (1968) MR0237027DOI10.1080/01621459.1968.10480919
  4. Kubáček, L., Kubáčková, L., Volaufová, J., Statistical Models with Linear Structures, Veda Bratislava (1995). (1995) 
  5. Kubáček, L., Multivariate Statistical Models Revisited, Palacký University Olomouc (2008). (2008) MR2796947
  6. Kshirsagar, A. M., Multivariate Analysis, Marcel Dekker, Inc. New York (1972). (1972) Zbl0246.62064MR0343478
  7. Mentz, G. B., Kshirsagar, A. M., 10.1081/STA-120022246, Commun. Stat., Theory Methods 32 (2003), 1591-1605. (2003) Zbl1184.62090MR1996796DOI10.1081/STA-120022246
  8. Rao, C. R., Mitra, S. K., Generalized Inverse of Matrices and its Applications, John Wiley & Sons New York-London-Sydney-Toronto (1971). (1971) Zbl0236.15005MR0338013
  9. Rao, C. R., Kleffe, J., Estimation of Variance Components and Applications, North-Holland Amsterdam-New York-Oxford-Tokyo (1988). (1988) Zbl0645.62073MR0933559
  10. Zellner, A., 10.1080/01621459.1963.10480681, J. Am. Stat. Assoc. 58 (1963), 977-992. (1963) MR0157439DOI10.1080/01621459.1963.10480681

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