Ridge Estimator Revisited

Lubomír Kubáček

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2012)

  • Volume: 51, Issue: 2, page 73-86
  • ISSN: 0231-9721

Abstract

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Bad conditioned matrix of normal equations in connection with small values of model parameters is a source of problems in parameter estimation. One solution gives the ridge estimator. Some modification of it is the aim of the paper. The behaviour of it in models with constraints is investigated as well.

How to cite

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Kubáček, Lubomír. "Ridge Estimator Revisited." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 51.2 (2012): 73-86. <http://eudml.org/doc/247129>.

@article{Kubáček2012,
abstract = {Bad conditioned matrix of normal equations in connection with small values of model parameters is a source of problems in parameter estimation. One solution gives the ridge estimator. Some modification of it is the aim of the paper. The behaviour of it in models with constraints is investigated as well.},
author = {Kubáček, Lubomír},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {linear model; ridge estimator; constraints; linear model; ridge estimator; constraints},
language = {eng},
number = {2},
pages = {73-86},
publisher = {Palacký University Olomouc},
title = {Ridge Estimator Revisited},
url = {http://eudml.org/doc/247129},
volume = {51},
year = {2012},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Ridge Estimator Revisited
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2012
PB - Palacký University Olomouc
VL - 51
IS - 2
SP - 73
EP - 86
AB - Bad conditioned matrix of normal equations in connection with small values of model parameters is a source of problems in parameter estimation. One solution gives the ridge estimator. Some modification of it is the aim of the paper. The behaviour of it in models with constraints is investigated as well.
LA - eng
KW - linear model; ridge estimator; constraints; linear model; ridge estimator; constraints
UR - http://eudml.org/doc/247129
ER -

References

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  1. Fišerová, E., Kubáček, L., Kunderová, P., Linear Statistical Models: Regularity and Singularities, Academia, Praha, 2007. (2007) 
  2. Harville, D. A., Matrix Algebra for a Statistician’s Perspective, Springer, New York– Berlin–Heidelberg–Barcelona–Hong Kong–London–Milan–Paris–Singapore–Tokyo, 1997. (1997) MR1467237
  3. Hoerl, A. E., Kennard, R. W., 10.1080/00401706.1970.10488634, Technometrics 12 (1970), 55–67. (1970) DOI10.1080/00401706.1970.10488634
  4. Hoerl, A. E., Kennard, R. W., 10.1080/00401706.1970.10488635, Technometrics 12 (1970), 69–82. (1970) DOI10.1080/00401706.1970.10488635
  5. Goldstein, M., Smith, A. F. M., Ridge–type estimators for regression analysis, Journal of the Royal Statistical Society, Series B 36 (1974), 284–291 (1974) Zbl0287.62036MR0418342
  6. Rao, C. R., Mitra, S. K., Generalized Inverse of Matrices and its Applications, Wiley, New York–London–Sydney–Toronto, 1971. (1971) Zbl0236.15005MR0338013
  7. Theobald, C. M., Generalizations of mean square error applied to ridge regression, Journal of the Royal Statistical Society, Series B 36 (1974), 103–106. (1974) Zbl0282.62055MR0368328

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