In this paper, we first investigate the estimation of the functional single index regression model with missing responses at random for strong mixing time series data. More precisely, the uniform almost complete convergence rate and asymptotic normality of the estimator are obtained respectively under some general conditions. Then, some simulation studies are carried out to show the finite sample performances of the estimator. Finally, a real data analysis about the sea surface temperature is used to illustrate the effectiveness of our methodology.
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The authors would like to thank the Editor in Chief, the A.E and the two anonymous reviewers for their insightful comments and suggestions, which have led to a great improvement of this present version. This research is supported by the National Natural Science Foundation of China (Grant Nos.: 72071068, 11901286), and Vieu’s research is partially supported by Spanish Ministerio de Economíay Competitividad (Grant No.: MTM2014-52876-R), which are acknowledged.
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Ling, N., Cheng, L., Vieu, P. et al. Missing responses at random in functional single index model for time series data. Stat Papers (2021). https://doi.org/10.1007/s00362-021-01251-2
- Functional single index model
- Uniform almost complete convergence rate
- Asymptotic normality
- Strong mixing dependence
- Missing responses at random