Minimax rate in prediction for functional principal component regression

Abstract

In this short paper, we consider the convergence rate of functional linear regression in prediction loss. For upper bound we consider estimation of the slope function based on functional principal component analysis. Lower bound is also obtained that shows the convergence rate obtained using functional principal component regression is optimal.

Keywords:

• Functional linear regression
• functional principal component analysis
• minimax convergence rate

2010 Mathematics Subject Classification:

• 62G20

Acknowledgments

We sincerely thank the AE and the reviewers for their insightful comments and suggestions which have improved the manuscript significantly.

Additional information

Funding

Yang’s research was supported by the National Nature Science Foundation of China grants 11471086 and 11871173, National Social Science Foundation of China grant 16BTJ032, National Statistical Scientific Research Center Projects 2015LD02, and Fundamental Research Funds for the Central University 19JNYH08. Lin's research was partially supported by NSFC, China (11701360 and 11571112).