Functional data has become increasingly popular in the recent statistical literature. Considerable attention has been paid to the development of functional data analysis. This thesis consists of four main chapters to address some important questions that arise from implementing FPCA in practice and to give answer to these questions. In Chapter 2, we investigate the problem of data preprocessing for functional data. We propose and analyzes a nonparametric functional data approach to missing value imputation and outlier detection for functional data. In Chapter 3, a functional naive Bayes classifier has been proposed for functional data which provides a surrogate density estimation for functional random variables that makes a direct extension of density-based classical multivariate classification approaches to functional data classification possible. In Chapter 4, we merge two ideas of functional classification and functional prediction to develop a dynamical prediction for functional data. The proposed functional mixture prediction approach combines functional linear model with functional naive Bayes classifier. In Chapter 5, we suggest a two-step segmentation procedure to estimate both the number and locations of the mean change-points of a functional sequence. Finally, the thesis concludes with a brief discussion of future research directions.
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