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Title: Regression with dependent functional errors-in-predictors Authors:  Cheng Chen - London School of Economics (United Kingdom) [presenting]
Shaojun Guo - Renmin University of China (China)
Xinghao Qiao - London School of Economics (United Kingdom)
Abstract: Functional regression is an important topic in functional data analysis. Traditionally, in functional regression, one often assumes that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by independent and identically distributed measurement errors. However, in practice, the dynamic dependence across different curves may exist and the parametric assumption on the measurement error covariance structure could be unrealistic. We consider functional linear regression with serially dependent functional predictors, when the contamination of predictors by measurement error is ``genuinely functional'' with fully nonparametric covariance structure. Inspired by the fact that the autocovariance operator of the observed functional predictor automatically filters out the impact of the unobserved measurement error, we propose a novel generalized method of moments estimator of the slope parameter. The asymptotic property of the resulting estimator is established. We also demonstrate that the proposed method significantly outperforms possible competitors through intensive simulation studies. Finally, the proposed method is applied to a public financial dataset, revealing some interesting findings.