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AStA Advances in Statistical Analysis

, Volume 103, Issue 4, pp 475–501 | Cite as

Estimation and variable selection for partial functional linear regression

  • Qingguo TangEmail author
  • Peng Jin
Original Paper
  • 107 Downloads

Abstract

We propose a new estimation procedure for estimating the unknown parameters and function in partial functional linear regression. The asymptotic distribution of the estimator of the vector of slope parameters is derived, and the global convergence rate of the estimator of unknown slope function is established under suitable norm. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Based on the proposed estimation procedure, we further construct the penalized regression estimators and establish their variable selection consistency and oracle properties. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about the real estate data is used to illustrate our proposed methodology.

Keywords

Partial functional linear regression Functional principal component analysis Variable selection Asymptotic properties 

Notes

Acknowledgements

This work was supported by the National Social Science Foundation of China (16BTJ019), the Humanities and Social Science Foundation of Ministry of Education of China (14YJA910004) and Natural Science Foundation of Jiangsu Province of China (Grant No. BK20151481).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and ManagementNanjing University of Science and TechnologyNanjingChina

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