Variance components and an additional experiment

Lubomír Kubáček

Applications of Mathematics (2012)

  • Volume: 57, Issue: 4, page 391-405
  • ISSN: 0862-7940

Abstract

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Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.

How to cite

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Kubáček, Lubomír. "Variance components and an additional experiment." Applications of Mathematics 57.4 (2012): 391-405. <http://eudml.org/doc/246487>.

@article{Kubáček2012,
abstract = {Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.},
author = {Kubáček, Lubomír},
journal = {Applications of Mathematics},
keywords = {additional experiment; variance components; insensitivity region; insensitivity region},
language = {eng},
number = {4},
pages = {391-405},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variance components and an additional experiment},
url = {http://eudml.org/doc/246487},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Variance components and an additional experiment
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 391
EP - 405
AB - Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.
LA - eng
KW - additional experiment; variance components; insensitivity region; insensitivity region
UR - http://eudml.org/doc/246487
ER -

References

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  1. Fišerová, E., Kubáček, L., Kunderová, P., Linear Statistical Models; Regularity and Singularities, Academia Praha (2007). (2007) 
  2. Chatterjee, S., Hadi, A. S., Sensitivity Analysis in Linear Regression, J. Wiley New York (1988). (1988) Zbl0648.62066MR0939610
  3. Giles, D. E. A., Srivastava, V. K., 10.1080/01621459.1991.10475063, J. Am. Stat. Assoc. 86 (1991), 441-444 1137127. (1991) MR1137127DOI10.1080/01621459.1991.10475063
  4. Kubáček, L., Kubáčková, L., Volaufová, J., Statistical Models with Linear Structures, Veda Bratislava (1995). (1995) 
  5. Kubáček, L., Kubáčková, L., Nonsensitiveness regions in universal models, Math. Slovaca 50 (2000), 219-240. (2000) MR1763121
  6. Kubáček, L., Kubáčková, L., Statistics and Metrology, Publishing House of Palacký University Olomouc (2000), Czech. (2000) 
  7. Neter, J., Wassermann, W., Kutner, M. H., Applied Linear Statistical Models, 3rd edition, Irwin Boston (1990). (1990) 
  8. Rao, C. R., 10.1080/03610927208827002, Commun. Stat., Part A---Theory and Methods 1 (1973), 1-8. (1973) Zbl0252.62037MR0315850DOI10.1080/03610927208827002
  9. 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
  10. Rao, C. R., Linear Statistical Inference and Its Applications, John Wiley & Sons New York-London-Sydney (1973); Czech translation: Academia, Praha, 1978. (1973) Zbl0256.62002MR0221616
  11. Rao, C. R., Kleffe, J., Estimation of Variance Components and Applications, North-Holland Amsterdam-New York-Oxford-Tokyo (1988). (1988) Zbl0645.62073MR0933559
  12. Rao, C. R., Toutenburg, H., Linear Models. Least Squares and Alternatives, 2nd ed, Springer New York (1999). (1999) MR1707290
  13. Seber, G. A. F., Lee, A. J., Linear Regression Analysis, 2nd ed, Wiley New York (2003) 0958247. Zbl1029.62059MR1958247
  14. Weisberg, S., Applied Linear Regression, 3rd revised ed, John Wiley & Sons New York (1980). (1980) MR0591462

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