Multivariate models with constraints confidence regions

Lubomír Kubáček

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)

  • Volume: 47, Issue: 1, page 83-100
  • ISSN: 0231-9721

Abstract

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In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can be used for confidence regions.

How to cite

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Kubáček, Lubomír. "Multivariate models with constraints confidence regions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 83-100. <http://eudml.org/doc/32474>.

@article{Kubáček2008,
abstract = {In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can be used for confidence regions.},
author = {Kubáček, Lubomír},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {multivariate model; constraints; variance components; plug-in estimator; insensitivity region; variance components; plug-in estimator; insensitivity region},
language = {eng},
number = {1},
pages = {83-100},
publisher = {Palacký University Olomouc},
title = {Multivariate models with constraints confidence regions},
url = {http://eudml.org/doc/32474},
volume = {47},
year = {2008},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Multivariate models with constraints confidence regions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2008
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 83
EP - 100
AB - In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can be used for confidence regions.
LA - eng
KW - multivariate model; constraints; variance components; plug-in estimator; insensitivity region; variance components; plug-in estimator; insensitivity region
UR - http://eudml.org/doc/32474
ER -

References

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  1. Anderson T. W.: Introduction to Multivariate Statistical Analysis., J. Wiley, New York, , 1958. (1958) MR0091588
  2. Fišerová E., Kubáček L., Kunderová P.: Linear Statistical Models: Regularity, Singularities., Academia, Praha, , 2007. 
  3. Kshirsagar A. M.: Multivariate Analysis., M. Dekker, New York, , 1972. (1972) MR0343478
  4. Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures., Veda (Publishing House of Slovak Academy of Sciences), Bratislava, , 1995. (1995) 
  5. Rao C. R.: Linear Statistical Inference, Its Applications., J. Wiley, New York–London–Sydney, , 1965. (1965) MR0221616

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