Multivariate statistical models; solvability of basic problems

Lubomír Kubáček

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)

  • Volume: 49, Issue: 2, page 53-67
  • ISSN: 0231-9721

Abstract

top
Multivariate models frequently used in many branches of science have relatively large number of different structures. Sometimes the regularity condition which enable us to solve statistical problems are not satisfied and it is reasonable to recognize it in advance. In the paper the model without constraints on parameters is analyzed only, since the greatness of the class of such problems in general is out of the size of the paper.

How to cite

top

Kubáček, Lubomír. "Multivariate statistical models; solvability of basic problems." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.2 (2010): 53-67. <http://eudml.org/doc/116514>.

@article{Kubáček2010,
abstract = {Multivariate models frequently used in many branches of science have relatively large number of different structures. Sometimes the regularity condition which enable us to solve statistical problems are not satisfied and it is reasonable to recognize it in advance. In the paper the model without constraints on parameters is analyzed only, since the greatness of the class of such problems in general is out of the size of the paper.},
author = {Kubáček, Lubomír},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Multivariate model; estimation; testing hypotheses; sensitivity; estimation; testing hypotheses; sensitivity},
language = {eng},
number = {2},
pages = {53-67},
publisher = {Palacký University Olomouc},
title = {Multivariate statistical models; solvability of basic problems},
url = {http://eudml.org/doc/116514},
volume = {49},
year = {2010},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Multivariate statistical models; solvability of basic problems
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 2
SP - 53
EP - 67
AB - Multivariate models frequently used in many branches of science have relatively large number of different structures. Sometimes the regularity condition which enable us to solve statistical problems are not satisfied and it is reasonable to recognize it in advance. In the paper the model without constraints on parameters is analyzed only, since the greatness of the class of such problems in general is out of the size of the paper.
LA - eng
KW - Multivariate model; estimation; testing hypotheses; sensitivity; estimation; testing hypotheses; sensitivity
UR - http://eudml.org/doc/116514
ER -

References

top
  1. Anderson, T. W., An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958. (1958) Zbl0083.14601MR0091588
  2. Fišerová, E., Kubáček, L., 10.1002/env.994, Environmetrics 20 (2009), 776–789. (2009) MR2838487DOI10.1002/env.994
  3. Fišerová, E., Kubáček, L., Kunderová, P., Linear Statistical Models: Regularity and Singularities, Academia, Praha, 2007. (2007) 
  4. Fišerová, E., Kubáček, L., Sensitivity analysis in singular mixed linear models with constraints, Kybernetika 39 (2003), 317–332. (2003) Zbl1248.62112MR1995736
  5. Fišerová, E., Kubáček, L., Statistical problems of measurement in triangle, Folia Fac. Sci. Nat. Univ. Masarykianae Brunensis, Mathematica 15 (2004), 77–94. (2004) MR2159120
  6. Giri, N. G., Multivariate Statistical Analysis, Marcel Dekker, New York–Basel, 2004, (second edition). (2004) 
  7. Kshirsagar, A. M., Multivariate Analysis, Marcel Dekker, New York–Basel, 1972. (1972) Zbl0246.62064MR0343478
  8. Kubáček, L., Statistical models of a priori and a posteriori uncertainty in measured data, In: Proceedings of the MME’95 Symposium, Selected papers of the international symposium, September 18–20, (Eds. Hančlová, J., Dupačová, J., Močkoř, J., Ramík, J.), VŠB–Technical University, Faculty of Economics, Ostrava, 1995, 79–87. (1995) 
  9. Kubáček, L., Criterion for an approximation of variance components in regression models, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 34 (1995), 91–108. (1995) MR1447258
  10. Kubáček, L., Linear model with inaccurate variance components, Applications of Mathematics 41 (1996), 433–445. (1996) MR1415250
  11. Kubáček, L., On an accuracy of change points, Math. Slovaca 52 (2002), 469–484. (2002) Zbl1014.62022MR1940250
  12. Kubáček, L., Multivariate Statistical Models Revisited, Vyd. University Palackého, Olomouc, 2008. (2008) 
  13. Kubáček, L., Fišerová, E., Problems of sensitiveness and linearization in a determination of isobestic points, Math. Slovaca 53 (2003), 407–426. (2003) Zbl1070.62057MR2025473
  14. Kubáček, L., Fišerová, E., Isobestic points: sensitiveness and linearization, Tatra Mt. Math. Publ. 26 (2003), 1–10. (2003) Zbl1065.62118MR2055178
  15. Kubáček, L., Kubáčková, L., The effect of stochastic relations on the statistical properties of an estimator, Contr. Geophys. Inst. Slov. Acad. Sci. 17 (1987), 31–42. (1987) 
  16. Kubáček, L., Kubáčková, L., Sensitiveness and non-sensitiveness in mixed linear models, Manuscripta Geodaetica 16 (1991), 63–71. (1991) 
  17. Kubáček, L., Kubáčková, L., Unified approach to determining nonsensitiveness regions, Tatra Mt. Math. Publ. 17 (1999), 1–8. (1999) MR1737699
  18. Kubáček, L., Kubáčková, L., Nonsensitiveness regions in universal models, Math. Slovaca 50 (2000), 219–240. (2000) MR1763121
  19. Kubáček, L., Kubáčková, L., Statistical problems of a determination of isobestic points, Folia Fac. Sci. Nat. Univ. Masarykianae Brunensis, Mathematica 11 (2002), 139–150. (2002) Zbl1046.62067MR1994204
  20. Kubáček, L., Kubáčková, L., Tesaříková, E., Marek, J., 10.1023/A:1023269321385, Application of Mathematics 43 (1998), 439–460. (1998) MR1652104DOI10.1023/A:1023269321385
  21. Kubáčková, L., Kubáček, L., Optimum estimation in a growth curve model with a priori unknown variance components in geodetic networks, Journal of Geodesy 70 (1996), 599–602. (1996) 
  22. Kubáčková, L., Kubáček, L., Bognárová, M., Effect of the changes of the covariance matrix parameters on the estimates of the first order parameters, Contr. Geophys. Inst. Slov. Acad. Sci. 20 (1990), 7–19. (1990) 
  23. 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, 355–372. (1967) MR0212930
  24. Seber, G., Multivariate Observations, Wiley, Hoboken, New Jersey, 2004. (2004) MR0746474

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.