Nonparametric Estimation in Functional Linear Model
We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y 1 yYn nare modeled in dependence of random functions X 1 X n. In the case of second order stationary random functions and as well in the non stationary case estimators of the functional slope parameter and its derivatives are constructed based on a regularized inversion of the estimated covariance operator. In this paper the rate of convergence of the estimator is derived assuming that the slope parameter belongs to the well-known Sobolev space of periodic functions and that the covariance operator is finitely, infinitely or in some general form smoothing.
KeywordsRandom Function Covariance Operator Nonparametric Estimation Functional Data Analysis Functional Principal Component
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