Marine Carrasco, Université de Montréal
Project Description/Abstract
In this paper, we consider a functional regression model where the predictor variable is a function and the target variable is a scalar. The main interest is to compare the Functional Principal Component Analysis (FPCA) and Functional Partial Least Squares (FPLS) techniques. We derive the convergence rate of the conditional Mean Squared Error (MSE) for both estimation methods and show that both methods display the same rate of convergence. Also, we show that this convergence rate is sharp. In addition, we find that for a fixed number of components, the regularization bias of the FPLS method is usually smaller than the one of FPCA approach, while the estimation error with the FPLS approach tends to be larger than that of FPCA and may explode as the number of retained components increases. Furthermore, FPLS tends to outperform FPCA in terms of prediction with a fewer number of retained components. Some Monte Carlo simulations and empirical evidence using the S&P 500 are provided to evaluate the performance of the considered methods.
Co-author
Idriss Tsafack, UC Irvine