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Multivariate regression model with constraints

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Mathematica Slovaca

Abstract

The aim of the paper is to present explicit formulae for parameter estimators and confidence regions in multivariate regression model with different kind of constraints and to give some comments to it. The covariance matrix of observation is either totally known, or some unknown parameters of it must be estimated, or the covariance matrix is totally unknown.

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References

  1. ANDERSON, T.W.: Introduction to Multivariate Statistical Analysis, J. Wiley, New York, 1958.

    MATH  Google Scholar 

  2. FIŠEROVÁ, E.— KUBÁČEK, L.: Sensitivity analysis in singular mixed linear models with constraints, Kybernetika (Prague) 39 (2003), 317–332.

    Google Scholar 

  3. KUBÁČEK, L.: Regression model with estimated covariance matrix, Math. Slovaca 33 (1983), 395–408.

    Google Scholar 

  4. KUBÁČEK, L.— KUBÁČKOVÁ, L.— VOLAUFOVÁ, J.: Statistical Models with Linear Structures, Veda, Bratislava, 1995.

    Google Scholar 

  5. KUBÁČEK, L.: Criterion for an approximation of variance components in regression models, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 34 (1995), 91–108.

    Google Scholar 

  6. KUBÁČEK, L.: Linear model with inaccurate variance components, Appl. Math. 41 (1996), 433–445.

    Google Scholar 

  7. KUBÁČEK, L.— KUBÁČKOVÁ, L.: Nonsensitiveness regions in models with variance components. In: 4th World Congress of the Bernoulli Society, Vienna, Austria, August 26–31, 1996, p. 281.

  8. KUBÁČEK, L.— KUBÁČKOVÁ, L.— TESAŘÍKOVÁ, E.— MAREK, J.: How the design of an experiment influences the nonsensitiveness regions in models with variance components, Appl. Math. 43 (1998) 439–460.

    Article  Google Scholar 

  9. KUBÁČEK, L.— KUBÁČKOVÁ, L.: Nonsensitiveness regions in universal models, Math. Slovaca 50 (2000), 219–240.

    Google Scholar 

  10. KUBÁČEK, L.— FIŠEROVÁ, E.: Problems of sensitiveness and linearization in a determination of isobestic points, Math. Slovaca 53 (2003), 407–426.

    Google Scholar 

  11. KUBÁČEK, L.— FIŠEROVÁ, E.: Isobestic points: sensitiveness and linearization, Tatra Mt. Math. Publ. 26 (2003), 1–10.

    Google Scholar 

  12. LEŠANSKÁ, E.: Insensitivity regions for estimators of mean value parameters in mixed models with constraints, Tatra Mt. Math. Publ. 22 (2001) 37–49.

    Google Scholar 

  13. LEŠANSKÁ, E.: Insensitivity regions for testing hypotheses in mixed models with constraints, Tatra Mt. Math. Publ. 22 (2001), 209–222.

    Google Scholar 

  14. LEŠANSKÁ, E.: Optimization of the size of nonsensitiveness regions, Appl. Math. 47 (2002) 9–23.

    Article  Google Scholar 

  15. LEŠANSKÁ, E.: Nonsensitiveness regions for threshold ellipsoids, Appl. Math. 47 (2002), 411–426.

    Article  Google Scholar 

  16. LEŠANSKÁ, E.: Effect of inaccurate variance components in mixed models with constraints. In: Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 11, Masaryk Univ., Brno, 2002, pp. 163–172.

    Google Scholar 

  17. RAO, C. R.: Least squares theory using an estimated dispersion matrix and its application to measurement in signal. In.: Proc. 5th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1. Theory of Statistics. University of California Press, Berkeley-Los Angeles, 1967, pp. 355–372.

    Google Scholar 

  18. RAO, C. R.: Linear Statistical Inference and Its Applications (2nd ed.), J. Wiley, New York, 1973.

    MATH  Google Scholar 

  19. RAO, C.R.— MITRA, S. K.: Generalized Inverse of Matrices and Its Applications, J. Wiley, New York, 1971.

    MATH  Google Scholar 

  20. RAO, C. R.— KLEFFE, J.: Estimation of Variance Components and Applications, North-Holland, Amsterdam, 1988.

    MATH  Google Scholar 

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Communicated by Gejza Wimmer

Supported by the Council of Czech Government J14/98: 153100011.

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Kubáček, L. Multivariate regression model with constraints. Math. Slovaca 57, 271–296 (2007). https://doi.org/10.2478/s12175-007-0022-7

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  • DOI: https://doi.org/10.2478/s12175-007-0022-7

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