Inversion of 3 × 3 partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters

Karel Hron

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 67-80
  • ISSN: 0231-9721

Abstract

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The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a 3 × 3 partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for 2 × 2 partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation of the mean value parameters in the twoepoch linear regression model with the nuisance parameters.

How to cite

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Hron, Karel. "Inversion of $3\times 3$ partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 67-80. <http://eudml.org/doc/32511>.

@article{Hron2006,
abstract = {The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a $3 \times 3$ partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for $2\times 2$ partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation of the mean value parameters in the twoepoch linear regression model with the nuisance parameters.},
author = {Hron, Karel},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {inversion of partitioned matrices; Rohde formula; twoepoch regression model; useful and nuisance parameters; best linear estimators of the mean value parameter; inversionof partitioned matrices; Rohde formula; nuisance parameters; best linear estimators},
language = {eng},
number = {1},
pages = {67-80},
publisher = {Palacký University Olomouc},
title = {Inversion of $3\times 3$ partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters},
url = {http://eudml.org/doc/32511},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Hron, Karel
TI - Inversion of $3\times 3$ partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 67
EP - 80
AB - The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a $3 \times 3$ partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for $2\times 2$ partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation of the mean value parameters in the twoepoch linear regression model with the nuisance parameters.
LA - eng
KW - inversion of partitioned matrices; Rohde formula; twoepoch regression model; useful and nuisance parameters; best linear estimators of the mean value parameter; inversionof partitioned matrices; Rohde formula; nuisance parameters; best linear estimators
UR - http://eudml.org/doc/32511
ER -

References

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  1. Harville D. A.: Matrix Algebra From a Statistican’s Perspective., Springer-Verlag, New York, 1999. MR1467237
  2. Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures., Veda, Publishing House of the Slovak Academy of Sciences, Bratislava, 1995. 
  3. Kunderová P., Locally best and uniformly best estimators in linear model with nuisance parameters, Tatra Mt. Math. Publ. 3 (2001), 27–36. Zbl1001.62021MR1889032
  4. Nordström K., Fellman J., Characterizations and dispersion-matrix robustness of efficiently estimable parametric functionals in linear models with nuisance parameters, Linear Algebra Appl. 127 (1990), 341–361. (1990) Zbl0709.62063MR1048807
  5. Štulajter F.: Predictions in Time Series Using Regression Models., Springer-Verlag, New York, 2002. MR1901566

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