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1. Optimal prediction for high-dimensional functional quantile regression in reproducing kernel Hilbert spaces

Author

Guangren Yang, Heng Lian, and Xiaohui Liu

Subjects
Statistics and Probability, Statistics::Theory, Numerical Analysis, Control and Optimization, Algebra and Number Theory, Logarithm, Applied Mathematics, General Mathematics, Hilbert space, Estimator, Upper and lower bounds, Quantile regression, symbols.namesake, Kernel (statistics), Linear regression, symbols, Statistics::Methodology, Applied mathematics, Mathematics, Quantile
Abstract

Regression problems with multiple functional predictors have been studied previously. In this paper, we investigate functional quantile linear regression with multiple functional predictors within the framework of reproducing kernel Hilbert spaces. The estimation procedure is based on an l 1 -mixed-norm penalty. The learning rate of the estimator in prediction loss is established and a lower bound on the learning rate is also presented that matches the upper bound up to a logarithmic term.

Published
2021