Abstract
We investigate kernel estimates in the functional nonparametric regression model when both the response and the explanatory variable (the covariate) are functional. The rates of almost complete and uniform almost complete convergence of the estimator are obtained under some mild \(\alpha \)-mixing functional sample. Finally, a simulation study is carried out to illustrate the finite sample performance of the estimator.
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Acknowledgements
The authors would like to thank the Editor in Chief, the A.E and the two anonymous reviewers for their valuable comments and suggestions that are very helpful for them to improve the quality and presentation of the paper significantly. Also, many thanks to Graduate student Li Lei Cheng for his help in some simulation studies. Ling’s work is supported by the National Social Science Funds of China (14ATJ005). Research of Vieu is partially supported by Grant MTM2014-52876-R from Spanish Ministerio de Economíay Competitividad.
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Ling, N., Wang, L. & Vieu, P. Convergence rate of kernel regression estimation for time series data when both response and covariate are functional. Metrika 83, 713–732 (2020). https://doi.org/10.1007/s00184-019-00757-y
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DOI: https://doi.org/10.1007/s00184-019-00757-y