Author Description

With the advancement of technology, the data we analyze have grown both in size and in complexity. The main interest of this dissertation is the estimation of optimal Tikhonov regularization parameter via leave-one-out cross-validation when applied to a large dataset. The model, to which Tikhonov regularization is applied, is a functional data regression model where both the predictor and response are functions. In the first chapter of this dissertation, we review several concepts and literature in functional data analysis, Tikhonov regularization, and the "divide and conquer" approach, which is often used to solve problems involving large amount of data. The second chapter will introduce two of our proposed algorithms that incorporate the "divide and conquer" approach in estimating optimal Tikhonov regularization parameter via leave-one-out cross-validation. Several simulation studies and application to electricity demand data will be presented to demonstrate the performance of the proposed algorithms.