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ABSTRACT
This paper studies M-estimation in functional linear regression in which the dependent variable is scalar while the covariate is a function. An estimator for the slope function is obtained based on the functional principal component basis. The global convergence rate of the M-estimator of unknown slope function is established. The convergence rate of the mean-squared prediction error for the proposed estimators is also established. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedure. Finally, the proposed method is applied to analyze the Berkeley growth data.
Acknowledgment
The author thanks two reviewers for their helpful comments and suggestions that led to improvements in this paper. This work was supported by the National Social Science Foundation of China (16BTJ019) and the Humanities and Social Science Foundation of Ministry of Education of China (14YJA910004).