Date of Award




Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

Content Description

1 online resource (viii, 107 pages) : illustrations (some color)

Dissertation/Thesis Chair

Igor G. Zurbenko

Committee Members

Igor G. Zurbenko, Karen Reinhold, Malcolm J. Sherman, Christian Hogrefe, Gregory DiRienzo, Mycroft Sowizral


eigenvalue, Kalman filter, multivariate analysis, ozone pollution, principal component, time series prediction, Atmospheric ozone, Noise, Noise pollution

Subject Categories

Atmospheric Sciences | Physical Sciences and Mathematics | Statistics and Probability


This thesis analyzes the effect of independent noise in principal components of k normally distributed random variables defined by a covariance matrix. We prove that the principal components as well as the canonical variate pairs determined from joint distribution of original sample affected by noise can be essentially different in comparison with those determined from the original sample. However when the differences between the eigenvalues of the original covariance matrix are sufficiently large compared to the level of the noise, the effect of noise in principal components and canonical variate pairs proved to be negligible. The theoretical results are supported by simulation study and examples. Moreover, we compare our results about the eigenvalues and eigenvectors in the two dimensional case with other models examined before. This theory can be applied in any field for the decomposition of the components in multivariate analysis.