2017/11/13 by Behdad Mostafaiy, Mostafaiy, Behdad, Mohammadreza Faridrohani +3
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1711.04854
openalex publication_date 2017/11/13 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper, we propose a novel approach to fit a functional linear\nregression in which both the response and the predictor are functions of a\ncommon variable such as time. We consider the case that the response and the\npredictor processes are both sparsely sampled on random time points and are\ncontaminated with random errors. In addition, the random times are allowed to\nbe different for the measurements of the predictor and the response functions.\nThe aforementioned situation often occurs in the longitudinal data settings. To\nestimate the covariance and the cross-covariance functions we use a\nregularization method over a reproducing kernel Hilbert space. The estimate of\nthe cross-covarinace function is used to obtain an estimate of the regression\ncoefficient function and also functional singular components. We derive the\nconvergence rates of the proposed cross-covariance, the regression coefficient\nand the singular component function estimators. Furthermore, we show that,\nunder some regularity conditions, the estimator of the coefficient function has\na minimax optimal rate. We conduct a simulation study and demonstrate merits of\nthe proposed method by comparing it to some other existing methods in the\nliterature. We illustrate the method by an example of an application to a well\nknown multicenter AIDS Cohort Study.\n