Discriminant coordinates analysis  in the case of multivariate repeated data

Mirosław  Krzyśko; Wojciech  Łukaszonek; Waldemar  Wołyński

doi:https://doi.org/10.21307/stattrans-2018-027

Discriminant coordinates analysis in the case of multivariate repeated data

Mirosław Krzyśko Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poland. Faculty of Management, President Stanisław Wojciechowski Higher Vocational State School, Poland , Wojciech Łukaszonek Faculty of Management, President Stanisław Wojciechowski Higher Vocational State School, Poland. , Waldemar Wołyński Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poland. Statistics in Transition new series, vol. 19, 2018, 3, pages: 495-506 Published online: 3 September 2018 https://doi.org/10.21307/stattrans-2018-027

214 Views 8 Downloads

ARTICLE

(English) PDF

ABSTRACT

The main aim of the paper is to adapt the classical discriminant coordinates analysis to multivariate repeated measures data. The proposed solution is based on the relationship between the discriminant coordinates and canonical variables. The quality of these new discriminant coordinates is examined on some real data

KEYWORDS

discriminant coordinates analysis, repeated measures data (doubly multivariate data), Kronecker product covariance structure, maximum likelihood estimates

REFERENCES

BANERJEE, S., ROY, A., (2014). Linear Algebra and Matrix Analysis for Statistics.CRC Press, Boca Ratop.

FISHER, R. A., (1936). The use of multiple measurements in taxonomic problem.Annals of Eugenics 7, pp. 179–188.

FUJIKOSHI, Y., ULYANOV, V. V., SHIMIZU, R., (2010). Multivariate statistics. High Dimensional and Large-Sample Approximations. Hoboken, New Jersey.GIRI, C. G., (1996). Multivariate Statistical Analysis. Marcel Dekker, Inc., NewYork.

GÓRECKI, T., KRZYSKO, M., WASZAK, Ł., WOŁY ´ NSKI, W., (2018). Selected ´statistical methods of data analysis for multivariate functional data, StatisticalPapers 59, pp. 153–182.

KRZANOWSKI, W. J., (2000). Principles of Multivariate Analysis, Revised Edition.Oxford University Press, Oxford.

KRZYSKO, M., (1979). Discriminant variables. Biometrical Journal 21 (3), pp. ´227–241.

RAO, C. R., (1948). The utilization of multiple measurements in problem of biolog ical classification. Journal of the Royal Statistical Society Series B, 10 (2), pp.159–203.

R CORE TEAM, (2015). R: A language and environment for statistical comput ing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R project.org/.

RENCHER, A. C., (1998). Multivariate Statistical Inference and Applications. Wi ley, New York.

SEBER, G. A. F., (1984). Multivariate Observations. John Wiley and Sons, NewYork.

SRIVASTAVA, M. S., (2002). Methods of Multivariate Statistics. Wiley, New York.

SRIVASTAVA, M. S., VON ROSEN, T., VON ROSEN, D., (2008). Models with a Kronecker product covariance structure: estimation and testing. Mathematical Methods of Statistics 17 (4), pp. 357–370