# Nonparametric Estimation in Functional Linear Model

• Jan Johannes
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

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.

## Keywords

Random Function Covariance Operator Nonparametric Estimation Functional Data Analysis Functional Principal Component
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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