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inversion of partitioned matrices; Rohde formula; twoepoch regression model; useful and nuisance parameters; best linear estimators of the mean value parameter
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.
[1] Harville D. A.: Matrix Algebra From a Statistican’s Perspective. : Springer-Verlag, New York. 1999. MR 1467237
[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. MR 1889032 | Zbl 1001.62021
[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. MR 1048807 | Zbl 0709.62063
[5] Štulajter F.: Predictions in Time Series Using Regression Models. : Springer-Verlag, New York. 2002. MR 1901566
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