Abstract

Functional data analysis holds transformative potential across fields

but often relies on mean regression, with limited focus on quantile regression.

Furthermore, the infinite-dimensional nature of the functional predictors necessitates the use of dimension reduction techniques. Therefore, in this work, we

address this gap by developing dimension reduction techniques for the conditional

quantiles of functional data. The idea is to replace the functional predictors with

a few finite predictors without losing important information on the conditional

quantile while maintaining a flexible nonparametric model. We derive the convergence rates of the proposed estimators and demonstrate their finite sample

performance using simulations and a real dataset from fMRI studies.

Information

Preprint No.SS-2024-0211
Manuscript IDSS-2024-0211
Complete AuthorsEliana Christou, Eftychia Solea, Shanshan Wang, Jun Song
Corresponding AuthorsJun Song
Emailsjunsong@korea.ac.kr

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Acknowledgments

Eliana Christou’s research was supported by the National Science Foundation under Grant No. DMS-2213140. Jun Song’s research was supported

Table 4: Average mean square error of local linear QR model using the first

dτ sufficient predictors constructed by FSIR and τ-FCQS.

Method

0.1

0.25

0.5

0.75

0.9

FSIR

5.18

4.75

4.53

5.89

7.95

τ-FCQS

4.26

5.21

3.84

5.42

6.93

by the National Research Foundation of Korea grants funded by the Korea government (MSIT) (No. 2022R1C1C1003647, 2022M3J6A1063595, and

RS-2023-00219212). The authors would like to thank the associate editor

and the two anonymous referees, whose comments lead to improvements in

the presentation of this paper.

Supplementary Materials

The online Supplementary Material contains additional assumptions, preliminary results and lemmas, proofs, and additional simulation results.

τ=0.25

τ=0.5

τ=0.1

y

y

y

Second predictor

Second predictor

Second predictor

Supplementary materials are available for download.