A study on regularized functional principal component analysis as a statistical dimension reduction technique

With modern technology, massive datasets can easily be scanned in the form of functional data. Functional data refer to data which consist of observed functions or curves evaluated at a finite subset of some interval. Functional data analysis techniques pioneered by Ramsay and Silverman are improved to analyses such type of data. Functional data analysis is an extension of traditional data analysis to functional data. Techniques in functional data analysis can be used to study the variation in a sample of functions xi, i=1, 2, ?, N, and their derivatives. In practice these functions are often a consequence of a preliminary smoothing process applied to discrete data. In this work, Spline Smoothing Methods are used. As the number of functions and the number of fields are increasing, it would be difficult to handle the functions altogether. Regarding this fact, in order to overcome this complexity, in this work, we utilize Functional and Regularized Functional Principal Component Analyses that have the capability of explaining a high percentage of variation with only a few components. Because of its flexibility of usage, functional data analysis has a comprehensive application area. In this dissertation an application in -MKB is given. Here -MKB 30 indice is examined from a different aspect and a new approach, the mean function, is proposed to demonstrate the general trend of the market.