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Title: Functional linear model with dependent regressors in high dimensions Authors:  Cheng Chen - London School of Economics (United Kingdom) [presenting]
Shaojun Guo - Institute of Statistics and Big Data, Renmin Unversity of China (China)
Xinghao Qiao - London School of Economics (United Kingdom)
Abstract: The functional linear model is one of the most widely used tools of functional data analysis. Existing approaches assume either independent and identically distributed functional regressors or a fixed number of dependent functional regressors. We propose a functional linear models to characterize the linear relationship between a scalar response and high dimensional functional regressors with serial correlation. We develop a penalized least squares approach to perform variable selection for serial correlated functional regressors. We investigate the theoretical properties of our proposed method under mild conditions and illustrate the sample performance through an extensive set of simulation studies and one real world example.