Στατιστικές τεχνικές ανάλυσης πολυδιάστατων δεδομένων και εφαρμογές
Statistical techniques for the analysis of multivariate data and applications
Βασιλειάδη, Βασιλική Ι.
Multivariate analysis deals with the collection, description and inference of data containing measurements of a large number of variables. Studying these variables independently may lead to conclusions that do not reflect the true nature and structure of the data because the dependence is not taken into account. Multivariate analysis explores the dependence between variables, combines them into groups and reduces their dimensionality thereof making them suitable for additional processing. The techniques that are used in multivariate analysis are graphical and statistical/mathematical. The graphical methods are used in the illustrative presentation of multivariate data thus facilitating the task of drawing some preliminary conclusions. Furthermore, the statistical/mathematical methods serve both the interpretation of the correlation between variables and the dimensionality reduction of the dataset being studied. The present dissertation initially provides an introduction in the most popular techniques of Multivariate Analysis. An extensive analysis of the main graphical methods is presented both in theory and application level. Moreover, it describes in detail, the most common statistical/mathematical multivariate methods. Finally, these methods are applied on a real dataset and an illustration is offered how one can derive useful conclusions by practicing the techniques described in the thesis.