Some asymptotic properties of functional linear regression model with points of impact

Document Type : Original Scientific Paper

Authors

1 Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

2 Department of Statistics, Faculty of Sciences, University of Zanjan, Zanjan, Iran

Abstract

The functional linear regression model with points of impact is a recent augmentation of the classical functional linear model with many practically important applications‎. ‎It is assumed that there exists an unknown number of impact points‎, ‎that is discrete observation times where the corresponding functional values possess significant influences on the response variable‎. ‎In this paper‎, ‎we obtain some asymptotic properties of the model that can be used for further statistical inferences about the response variable‎. ‎Specifically‎, ‎rates of convergence for eigenfunctions estimates of the predictor covariance operator evaluated at the impact points estimates are derived‎. ‎These are important results‎, ‎because we do not have true eigenfunctions and impact points in applications and we have to use their estimates instead.

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Journal of Statistical Modelling: Theory and Applications
Volume 3, Issue 1
January 2022
Pages 71-81

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History

  • Receive Date: 15 November 2022
  • Revise Date: 20 February 2023
  • Accept Date: 25 February 2023

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