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Penalized function-on-function linear quantile regression

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Abstract

We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic B-splines expansion is used to represent the regression parameter functions, where a derivative-free optimization algorithm is used to obtain the estimates. Quadratic roughness penalties are applied to the coefficients to control the smoothness of the estimates. The optimal degree of smoothness depends on the quantile of interest. An automatic grid-search algorithm based on the Bayesian information criterion is used to estimate the optimum values of the smoothing parameters. Via a series of Monte-Carlo experiments and an empirical data analysis using Mary River flow data, we evaluate the estimation and predictive performance of the proposed method, and the results are compared favorably with several existing methods.

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Acknowledgements

We would like to thank an Associate Editor and two reviewers for their careful reading of our manuscript and for their valuable suggestions and comments, which have helped us produce an improved version of our article. The second author thanks financial support from an Australian Research Council Discovery Project DP230102250.

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Authors and Affiliations

  1. Department of Statistics, Marmara University, 34722, Kadikoy, Istanbul, Turkey

    Ufuk Beyaztas & Semanur Saricam

  2. Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW 2109, Australia

    Han Lin Shang

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  1. Ufuk Beyaztas
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Correspondence to Ufuk Beyaztas.

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Example scripts for the Monte-Carlo experiments and the empirical data example are available at https://github.com/UfukBeyaztas/pflqr.

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Beyaztas, U., Shang, H.L. & Saricam, S. Penalized function-on-function linear quantile regression. Comput Stat (2024). https://doi.org/10.1007/s00180-024-01494-1

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